Look up some of RealKingCobra's posts....I know there have been threads on here that talk about the angle of the pocket and how it must match with the pocket size or it will cause balls to rattle like crazy.
I've got 4 3/8 " pockets, and I don't have any issue hitting balls down the rail. I can slow roll or hit it a million miles an hour and it will drop.
It could be that the angle of the pocket opening and/or the down angle of the pocket facing don't match up with the size of your pockets.
Something to look into if you haven't already.
Absolutely this!
How did your mechanic go about tightening your pockets? Did he just glue a bunch of extra pocket facings on, or did he extend the subrails? Even aside from the pocket angle issue (which is huge), you technically could have pockets cut to an ideal angle, but if there's 3/4" of soft rubber either side of your pocket, it's not surprising that you're getting balls rattling out. And if that's the case, it's not even any better of a One Pocket table either, since you don't have any more effective rail to work with for banks close to the pockets (just an unpredictable, monster pocket point that extends too far up the rails, if you follow me).
Use the search function to pull up RKC's posts on this, as Wheels suggested, and also Mark Gregory's posts. As Wheels pointed out, if balls well hit down the rail are rattling out, something is very wrong.
But recognizing that you have a problem is the first step to recovery, lol. I don't know what kind of budget you're working with, but a home table that plays like crap is going to turn you into a bowler faster than anything. You already invested in the table. Sending your rails off to someone like Mark Gregory will have you weeping with joy once you get them back, after what sounds like months of frustration. He made me an Anniversary out of walnut with 4.25" pockets and while it's tough as hell for me (I'm no A-level player), it has zero rattle and so long as I do my part and put the ball between the points, it'll fall - even at break speed.
Lots of far more knowledgeable posters have already made compelling arguments for why sub-4.5" pockets fundamentally change the game in some detrimental ways, particularly if you're not predominantly a one-holer. Wouldn't presume to disagree. However, since you've clearly made a commitment to having tight pockets, there IS an argument for you following through, which is that if you just have your mechanic scrape off the extra pocket facings and return your table to standard, this may well foster a phobia of tight pockets.