It actually depends on the planning,
13 months span cover from launching to commissioning, probably Chinese shipyard launches the vessel with all systems are integrated on (electronics etc). The time took from first steel cut to commissioning of the first vessel of any order, only this, would tell us the true span about building. This is rather hard to describe in words, but modules of the ships can be built in parallel, 4 ships would take 4 years, but 1 ship alone would take 2.5 -3 years.
This is a preference they can either launch ship equipped if they have enough space ( on drydock-slipway) or launch it bare, tow to the berth or another dry dock (if requires dry works) and equip it in there. It depends on the size of shipyards, crane arrangements, production flow and bunch of other stuff those i don't know.
They have larger shipyards with more steel processing capacity, more automated in terms of steel processing but system integration (equipping) is entirely relies on handwork,and sometimes it is not done in parallel with steelworks or even within themselves, this is valid for testing as well not all procedures can be conducted in parallel. Briefly i can say this: comparing any ship's launching to commissioning timespan does not give any insight about the time it is built unless we know how the shipyard works. But 13 months for steel construction+equipping+remakes+testing doesn't make much sense, it is rather impossible. it is for sure, partially equipping (minor things like furniture that can be equipped in between of testing)+testing to take 13 months.
I know at least one Korean shipyard installs (equips) the steel modules (blocks) before erecting (mounting) this requires high accuracy manufacturing and experience but i am not again sure if this could be achieved in naval vessels, considering mass amount of cabling-piping, but i know our shipyards ,except a few, can not work with large blocks; the smaller blocks are, the more time spend on erecting them. It is simply far more easy to build those blocks on the ground than mounting smaller ones to each other on the slipway.
Assuming China has built enough many warships to gain experience on this as well. This could be another factor to accelerate their progress. They are much more experienced than us in this. However, All aforementioned factors wouldn't double their production speed. It would only accelerate when multiple ships are delivered in a row.
Before 2010 i personally knew people who has avoided Chinese shipyards and leaned on Japan and Korea due to multiple reasons. But nowadays they are good as Koreans and they have already gained majority of the pie and also trusted by shipowners. As of 2020, especially for a Chinese military shipyard, we can hardly speak of low quality production (at least i can say this for steelworks). They spend a lot on R&D. Hundred folds of our research budget for ship design, production, engineering related jobs is poured on the universities.
Last matter, China (or Chinese shipyard) considers this in terms of profit, the sooner they finish and deliver the vessel the more profit they will gain. We consider this in terms of providing ships to a country that our government refers as brother.
One more brief explanation, i have came across a few guys complaining about schedule of this project in almost in threads related to J-Class:
Pakistan ordered Type 54A Frigate in 2018 June, This is a ready to built platform for Chinese and maybe with minor modifications that can be applied (for the PN requirement like Galley- berthing - prayer room and so on) on the go, and first ship will be delivered in 2021 Q2 (Q3 or Q4) which takes about 2.5 years or 3 or more; without any ToT. This simply proves a Type 54A is not built within 13 months.
For F22P the first ship roughly took about 3 years in China, again we don't know when steel cut has started, only keel laying is indicated,in the same way the last ship which is built in Pakistan took about 3 year. For the last ship of the J-Class it is expected to lay keel 18 months after the 1st ship, which will be 2022 and delivered in 2025, which is again 2.5-3 years.
Pakistan has ordered J-Class in 2018 (or 2019 i am not quite sure), with accepting that design modifications applied on Ada-Class will take 18 months or even longer (since Pakistan has also joined on this process). Turkey or any other country is in no place to prepare a design in details just for possible 4 ships purchase. Moreover, Turkey has offered ToT, probably far more than what Chinese has offered within F-22P project and furthermore one vital thing : Ability to design warships, IP rights of the new design and system integration viable for future, The furthest ToT shipbuilders has offered were extending to module building, block erecting and production phase in most of the cases (speaking of purchases and deliveries made by other countries). Turkey has spent years or decades to gain this knowledge, and we are sharing this for sake of brotherhood, not the finances.
Last words: The single matter is how countries' authorities came into agreement, it could have been 10 or 20 year, it all what depends on. There are multiple reasons to settle a schedule, finances, extension of the ToT, Navy's requirement and procurement-replacement schedule-training of personnel is only a few factors. Chinese shipyard can equip (the numbers are just fictitious to make some point) 4 ships in parallel for foreign sales, considering the sources they have got and the huge demand for their own navy, our military shipyard can spare only 1 slot for foreign sales to ensure 1-2 slots for our own demand. Even for I-Class's 2nd-4th vessels a consortium is spoken of, to produce more ships in shorter times.