Tag Ups - Time Play not a Force Out

[Canary]

Okay guys I'm not a umpire so don't scream at me for this.

From the ASA Rule book:

K. Tag-Ups. When a runner leaves a base too soon on a caught fly ball
and returns in an attempt to retouch, this is considered a time play and
not a force out. When the appeal is the third out, all runs scored in
advance of the appealed runner and prior to the legal appeal count.

Is this saying, you have to tag a runner when they try to come back after a caught fly ball?

Does a "time play" dictate only the base needs to be tagged, or does it imply the runner must be tagged?

Because we have always tagged the base "only".