There are a couple of problems.

One is that the constructor, regardless of how much damage it has taken, disappears, and "becomes" the starbase.

Two is that the starbase has shield mitigation while it is being constructed.

Three is that it takes somewhere in the vicinity of 300 DPS to take out a starbase before it finishes being constructed (on fast, anyway), assuming you start firing on it as immediately as possible.

Three is largely but not entirely the fault of two.

Four is the fact that starbase construction times in general and starbase construction times in hostile gravity wells in particular are way too fast.

As for constructing in the presence of a Vasari starbase, while targeting priority probably needs to be looked at, I'd assume that the AI didn't do one or both of the weapons upgrades.

They're not supposed to be defensive. Deploying them in a hostile grav well is a valid and planned tactic for them.

The Vasari do get a slightly unfair advantage there because theirs moves (I'd be perfectly happy making theirs not move) which means they can deploy the Migrator as soon as it jumps in and before the defensive fighters can destroy it. So it can immediately deploy on the edge of the grav well and then the constructed starbase moves into range.

The other races don't have this because they need to deploy it in a place that matters. And their deployment cruisers are paper thin, which means against any competent player they really should never get in place to deploy