How long do I have to wait to receive a compensation from Turkish Airlines?

On Monday, 17/07/2017 I was flying from Tbilisi (TBS) to London (LHR) via Istanbul (IST). The transfer in Istanbul was 1:30 - more than enough in my experience, as I've flown this particular combination of flights a number of times.

The flight from Tbilisi left about 15 minutes late - I didn't think much of it - however it arrived about 1:20 late into Istanbul. Then it didn't taxi to the gate but instead we were transferred to the terminal by coach. With security, etc. there was no way I would be able to make the connection to the UK flight in under 10 minutes - so I missed the flight. Unfortunately, that was the last flight of the day and I was stuck in Istanbul overnight. I eventually arrived to London almost 12 hours later than my scheduled flight.

Turkish Airlines did provide hotel accommodation in Istanbul and a transfer to/from the hotel, but that was it. They did not pay for any meals (the argument was that all places that accept their vouchers are closed and won't reopen until after the morning flight leaves) and I had to pay £20 for the visa to exit the airport. I was given the compensation brochure that states the standard EU rules for compensation (i.e. €400 compensation plus hotel, meals, etc.) The brochure also provided info on how to claim such compensation - via their website.

Overall, I spent GBP 20 on the visa, another TRY 25 on some food in Istanbul plus I had to pay GBP 25 in London for late pickup of a car from the parking. I also lost half a day at work - essentially loosing money on that, too.

I submitted the compensation per their instruction, with all details and attaching all receipts. This was on Tuesday, 18/07/2017. I have not heard back. I contacted them again via that same web site on Friday. Again, I still haven't heard back from them.

I read somewhere that the compensation should be paid within 7 days of the claim (I wish I remembered where exactly I saw this), yet 5 days after my claim, I haven't even received an acknowledgement of it. How long normally should this take (ideally from experience with Turkish). Do I need to keep reminding them every few days?