Full joists are typically lapped on a beam. Splicing a joist that cannot reach the beam in full is absolutely not permissible by code. However, since it already exists, I would doubt that the inspector would require replacement. But then again he/she may be doing a little schooling with his/her inspector badge on since it sounds like you are an owner doing your own work. A possible hint to me was the plastic under the plate; the PT plate not so much (I've seen it done with and without PT but "per code"?). If anything, he/she should require that the plate be glued when fastened which, obviously, cannot be done with plastic in between.
This goes back a few years but when I put a kitchen addition on our house (did everything but the excavation and the foundation), the electrical inspector required that I add what are called a "ball box" extension to the sides of some of my metal electrical boxes (provides more volume in the box for receptacle sized wires). Two of my uncles, who were electricians, helped me with the installation and have never heard of such a thing. I had no choice and reluctantly complied.
You can go to the township and look through their building codes. Maybe a local library has the BOCA codes to take a gander but they are a little lengthy. But then you're building a clock instead of asking for the time. Others on this forum are sure to know and will make suggestions.
Good luck.
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