They should have checked all t-moldings before the adhesive set up. Weights work well providing it's balanced and distributed evenly. Small wedges also work well under a closed door.

Any difference in the tile and hardwood height?

Hard to believe the oozed adhesive wasn't cleaned up right away. There's a chance the bad areas can be carefully removed and re-installed.

I would make sure they clean up all that glue, and if there is damage under it, that they do all repairs before they leave. The one moulding with the gap, in your first picture, does not look right to me.

They used polyurethane glue with entirely predictable results. The question is: "Why"?

You can use double stick tape, make sure it's rated for flooring transition strips. . Faster and cleaner compared to the liquid nail they used.

How did they not notice the glob of glue and did nothing about it?

Thank y’all for your feedback! They came back and cut away the glue, and they will remove the t-molds and re-glue them.

Why are they glued in the first place. T mouldings come with a metal track, that is attached to the sub floor, and with the required distance between where both floors end. The t moulding snaps on right over the top of it. I have 6 of them in my house. They have been there for many years, with no problems at all, and not a bit of glue.

It looks to me like they used a "gorilla glue" type of glue - that expands after application. Either they didn't have experience with what they were using or accidently brought the wrong product (it seems like the wrong product altogether, IMO). That is probably why they tried to weight down the strips, because they saw them lifting from the glue expansion.

OP, were these guys supposed to be pros?