Cleared to the middle of STAR. When to descend?

I was flying to KDAB during the recent Daytona Beach event. Filed TTHOR3.KYLEG arrival.
Traffic was quite heavy so I was given delay vectors and speed restrictions.
Finally I was cleared “Direct to TTHOR, descend via TTHOR3 arrival, resume normal speed”.
At this moment I was at FL260 ~70nm from TTHOR. ToD was calculated at ~40nm from TTHOR.
So I turned direct to TTHOR and was flying at FL260. Approx 55 miles from TTHOR, center called me, said that I was supposed to descend long time ago, gave me another heading and directed to descend to 16000.

Was I supposed to start a shallow descend to arrive to TTHOR at 12000? Or flying to ToD and then doing normal descend is correct procedure?

Frequency was rather busy so I didn’t want to bother controller at the time.

Hmm… I’d see this as a couple of problems. First you were given delay vectors and speed restrictions. That’s fine and dandy there. However

Cleared direct TTHOR, descend via the TTHOR3 Arrival

This effectively takes you OFF of the STAR, so any descent instructions prior to TTHOR would have to come from the controller, especially since you have a hard crossing restriction of 12000 at TTHOR.

Resume normal speed

This would be a bit redundant here, as if being given “descend via”, that authorizes you to descend via the arrival, plus comply with all altitude and speed restrictions.

What should have happened here is when being cleared direct to TTHOR, that’s fine; however, you should have been given the crossing restriction, followed by the descent clearance:

Cross TTHOR at 12000, then descend via the TTHOR3 Arrival.

That would authorize you to descend at any point, as long as you cross TTHOR at 12000, then descend via the arrival. Being cleared direct to TTHOR then descend via the STAR cancels the entire STAR along with the crossing restrictions along it until you get to TTHOR, so you were stuck to begin with.