Yes, it definitely depends on the type of garlic and variety. Both daylength and temperature will have some effect on when they form scapes (if hardneck), when they start to bulb, and when ready to harvest.
I think temperature is more important for garlic than a specific day length, at least ours can be delayed for a week or more in putting out scapes, which is when they start to bulb after you take them off afaik. And a difference of as much as 3 weeks in when they are ready to harvest, depending on the weather that season.
This Texas page says your crop should mature in June.
https://bexar-tx.tamu.edu/homehort/a...e-week/garlic/
Here is another word about temperatures:
"Day-length as well as accumulated growing degree days determines when scapes appear as well as when bulbs are ready to harvest. Hot weather above 91°F (33°C) ends bulb growth and drying down starts. It’s irreversible. It is important to get plenty of good rapid growth before hot weather arrives."
https://www.sustainablemarketfarming...ulb-formation/