I presume (but this is guess work), that the change happened because the IPS was a state printer and Petiti a commercial one which probably wasn't politically bound to refuse work from central powers (or felt no moral pangs to do so).
I spent a few hours yesterday working on these. As far as I can see from the catalogues, Bradbury Wilkinson continued providing the dies right through the first world war so no conflict between politics and business there. As the 1911 and 1915 stamps are quite different I have to wonder why they needed to re-engrave the dies after only four years. Plates wear our but can usually be replaced without needing new dies. The only thing that makes some sense to me is that BW sent the dies to Rome and the Government printer produced the printing plates. Then when war broke out, the government printer refused to release the dies to Petiti which meant sourcing new ones from BW. The next recess set in 1921 were printed as well by BW but who printed the 50st Tirnovo City stamp in deep blue which only seems to appear with the 3l overprint in 1924? By this time, the Government Printing Works in Sofia were printing Bulgarian stamps but they don't seem to have had a recess capability.