This phenomena is something I see in my engine as well.
During the opening phase it produces very high scores, on many occasions the scores are getting so high that it will sacrifice a pawn without any real compensation.
In the current TCEC tourney my engine lost several games due to this.
My mistake is that I never tested the engine without opening book, and I never tuned the engine for opening play.
At the moment I'm looking at it, these high scores are indeed coming from the PST.
To solve this I have to scale the PST a lot lower, or the piece values a lot higher, during the opening phase.
This means that I have to retune everything.

I will probably leave it like it is, and spend my time to continue working on my new engine.
Sometimes I have the feeling that the whole concept of PST is flawed, and that the (added) value of a piece should solely be determined by the positional evaluation.