Why are the leaves of transplanted tomato seedlings curling upwards?

Question

I am trying to grow San Marzano tomatoes from seed and having no prior experience in gardening, every step just ends up becoming an experiment.
I sowed the seeds in a home-made potting mix containing

• Coco peat
• perlite
• sand (without it coco peat seemed to be retaining a lot of water.)
• NPK 20-20-20 (trace amounts)

Unfortunately, the lack of direct sunlight resulted in leggy seedlings but I was able to correct the situation a bit by placing the seeding tray outside.

Now, I am trying to transplant these seedlings into a bigger container to support the long stems and help develop a better root system. This bigger container is about 6-7 inches deep and contains

• coco peat
• perlite
• garden soil
• compost

This is where things are going wrong. About 24 hours after the transplant the leaves of the seedlings are curling upwards or in some cases turning dark green and crispy like a roasted herb. As we can see in the following images, the veins in the seed leaves are also turning yellow.

I am trying to keep the soil generally moist. The transplants are protected from direct sunlight but they are getting plenty of light and light breeze.
I would really appreciate it if anyone could tell me the things I might be doing wrong and steps to recovery.

The temperature is consistently in the 25-33 °C and is expected to be stable for a couple of months. There is also mild rain every 4-5 days.
Thank you in advance.

UPDATE (9 August 2020):

This morning I found the transplanted seedling fallen sideways. Gentle prodding revealed that the entire stems had perished.

It may have been excess fertilizer in the soil or excess moisture or even pest.

STEPS TAKEN: I am preparing a fresh batch of the potting mix using:

• perlite
• coco peat
• compost
• garden soil

And will try to transplant 1 seedling.

Answer 1

Let's keep it in indirect sunlight for a couple of days and see how it recovers. Inportant is that the upper and new leaves look green and healthy. I think by transplanting the plants some roots got damaged and it was not able to take up enough water and the lower leaves started to curl.

These lower leaves won't get better anymore, but don't worry new ones will form if it is recovered. Also, you can put the leggy plants a bit deeper in the pot than the seedlings were initially, the stems in the ground form new roots easily.

When recovered (healthy new growth) put it in the sun again and water it daily with these temperatures.

Last comment, I wouldn't used garden soil in pots. Coco peat and compost mixed with perlite sounds very good.

Answer 2

Soil looks damp.

Leggy plants might have this kind of transplant shock

Yellow/roasted leaves could be due to, over fertilizing or over watering.