Firstly, am I correct in assuming that if a user purchases two (or more) plans at the same time, then the URL’s for each plan are triggered?
Yup.
Secondly, if so, in which order are they triggered?
Given multiple plans are subscribed at the same time then they're triggered in the order the plans are in on CBSubs > Plans I believe.
We have master and child plans – would the URL for the master plan always be triggered before the child plan?
I believe so, yes.