Runner fails to tag - dead ball is called....???

[MechanicGuy]

Odd situation last night. Mens slowpitch.

Runners on FIRST and THIRD, 0 Outs.

Liner at the feet of the 3B, but caught. Home plate ump clearly calls him out. Both runners had taken off on contact. Defenders make the play on the runner going home.

Now the fun part...

The runner on first headed to second and stopped there, looking a little unsure of what was happening. Home plate ump calls time. At this point, the runner on second realizes he should've tagged up but didn't. He walks back to first base.

I, in the field, tell him he has to stay at second because time was called and the ball is dead. The fielders protest, and then realize what's going on, so they appeal at first and I call him out.

Was this handled correctly? Other umps at the field agreed that it was.