If the boost kicks in at 3000rpm then it's very likely that the actuator of the variable turbine blades isn't working as intended because at this engine speed the pressure from the exhaust is high enough to get a significant boost even without working VTG. It could be stuck or the actuator itself is broken.
I've found a nice cut-through of this part here: [first post, first image]
https://f30.bimmerpost.com/forums/showthread.php?t=215197This might be also related to broken or blocked VTG blades but if the turbo was completely refurbished it's unlikely that the mechanics in charge forgot about this because you need to pop out the whole intake body to replace the shaft.
It would be helpful to know which exact engine you have in your car because older models rely on vacuum controlled actuators for which other solutions may apply.
In any case it would help to contact somebody who has the ISTA-D software at hand. There is a turbo related and an air intake test routine that checks everything from air intake (MAF) down to exhaust (O2 sensor).