I'm a long time gardener also and only started mulching seriously last year. We live in zone 3 in Western Canada so can't mulch very early. Haven't done it yet as I wait til the perennial "babies" that have self-seeded are up enough to either transplant or pull as weeds.

Watching the news I see you are having a heat wave so it might be time to mulch so you don't have to water as much.

I have mulched with straw for some years now and apply it as soon as possible after transplant. (OP tomatos)
The only detrimate I have found is there are lots of what I believe are aphids that must stay in the bales while they are in the barn.
Lots of small pinholes in the lower leaves as the grow. Ours are about two and three feet tall now.
I need to introduce lady bugs to the garden soon for this and am waiting to see what effects the compost tea has to pests.
A few grass or straw seeds come up, but the suppression of weeds and soil splash are of more importance IMHO.

Yesterday, today, tomorrow. When ever you have the material to mulch with and the time to apply it is fine. I know there are those that say you should not mulch until the soil is warm, but I have not found that to be a problem here and I have mulches on the planting beds from late fall until mid August, when the soil bacteria digest all the mulch.

I'm on the thought that if it's something that needs heat to get going, and you're having a cool spring (like we are, cool and wet), I would hold off until the weather is sufficiently warm. I think it was in one of Lois Hole's gardening books, saying if you mulched too early, it could keep the soil temperatures cooler longer - this wouldn't be a good thing for heat loving plants, like cukes and pumpkins and such. Great for peas, I try to mulch mine as soon as they are up, since they like their roots to be cool.