Oh this is going to be an adorable an soft quilt!!
I understand you are newer to quilting than garment sewing - do you chain piece? This was a new concept to me when I moved into quilting. Quilting is a very different realm of sewing (as already stated) with its own set of guidelines. These are likely not matching up because first, you may not be sewing at an accurate 1/4" seam using your serger...and second...most sergers trim away excess so if you make a "whoops!" there's no getting that fabric trimmed away back!
Probably the biggest difference between quilting and other kinds of sewing is the math. Unless you're entering shows you don't have to be absolutely machine perfect...only as perfect as YOU want to be...however, you do need to be at least relatively accurate or you'll have the issues you're having now - things don't line up.
The best thing you can do to start is - use your 1/4" foot (or measure 1/4" from your needle to a point on your needle plate and mark it) - be consistent. Chain piecine will really help with speed - and that serger, while we love it for other kinds of sewing, I would suggest to set it aside for quilting. I have been quilting for ten years and have created a business out of my passion - I STILL make mistakes and need the flexibility of being able to open up those seams.
Another thing - have you heard of "nesting" seams when you match up your blocks? Try pressing seams in oppose direcitons, the when you match up two seams for perfect points, nestle the "hump" of each opposite side against the other (with right sides of fabric together). If you google "nesting seams quilting" you will get some pictures to really help you understand what I mean.
You have moved from the East Coast to the West Coast in the world of sewing!!
My Mother is a very skilled garment sewer - but comes to me still for questions regarding quilts! You will do wonderfully very quickly because you already have the skillset and you are just applying it differently. Good luck!