Correct call?

[Monguila]

Please help me with this call.

Batter/runner beats the throw to first, but misses the base. The umpire calls him safe. On his way back to first, he is tagged and the umpires signals safe again. The manager comes out to argue and the umpire says: "can not do your job for you, coach. Play ball." Before the next pitch, the play is appealed at first, and the runner (previous batter) is called out.

Did the umpire get it right?

Thanks in advance,

Luis