I used blue painters tape and marked out my lines in bathroom. I made sure they were level, and used a flat edge to really press down edgesof tape. How come I get leak through paint under the tape on the edges? What am I doing wrong?

I am having a bathroom gutted. They are almost done...I am talking with my wife and apparently the wallboard guy came and finished sanding today. The plumber also came today to put just about everything-toilet, sink, shower faucet, back together. I asked the contractor to let me know when I could prime. He didn't let us know when we could paint. The opening for the vanity is about 32.5" wide. The vanity is 30" wide. My wife says she can see the green wallboard. The plumber said I could put the brush between the vanity and wallboard. I asked if I could move the vanity back out, but obviously with the sink being connected, this would be a problem. I know the paint will get on the vanity side walls when I do this! :wall: How important is it to paint (at least prime?) the greenboard?