As PU in this situation, I will come up the line and watch the play develop.
If we have a fly ball and a possible tag up situation at third, I'll move up the line, read the play, and take the tag up at third if this develops. As I come into position, I let my BU know with "I have third IF he tags". This is an advance mechanic.
And, on a slow developing play in the infield where the first play goes to first base, I will come up the line and take the second play at third. Again, you must read the situation and the play BEFORE you commit.