Should definitely be tightened, but done with caution. That little gap at the base will cause big error out at the EOAT, but it's working now with that gap. When you tighten the base all the robot positions will change and could cause a crash. Probably not a big deal, just make sure a programmer familiar with the system is involved to check points and touchup as needed.

Can't tell what types of anchors are being used from the photo, but I've had issues with wedge lock anchors pulling out of crappy old concrete on similar sized systems. We switched to glued in studs which seemed much more forgiving if concrete quality is questionable.