Best way to fix Boost Spike when fitting 4" Dump pipes to Fg Turbo / Territory Turbo

Can boost be limited with retune when a 4" dump has been fitted, or do the waste gates need to be ported / or even a external wastegate fitted?

2011 XR6T Manual. After fitting 4" dump pipe its loses boost when changing 2-3rd gear under hard acceleration, and then wont boost again until its been turned off for awhile. Only other mod is sports exhaust, 50% atmo blow off valve, and slightly bigger intercooler

2007 Territory Turbo. Only mods are a 4" Dump and sports exhaust and seems to now be boosting/spiking to 15psi and hitting some type of boost cut, but once it drops down starts boosting again.

Thanks

Yes, tune will fix it, or put the stock Cat back in.