CFII reported receiving a 'low altitude alert' from ATC while conducting a localizer approach with a student. Approach was continued to a landing despite the CFII's warning to student of descent below VASI guidance.

Narrative

I'm a CFII currently training a student for their CFII. We are both IFR current with recent instruction in actual IMC and the student had fairly recent actual IMC experience. The student filed IFR for a short round robin flight with a couple LOC approaches for partial panel practice from the right seat. ATC cleared us for 3000' and we entered the broken layer at 2000'; so we were in and out of IMC with intermittent ground contact. The student executed a LOC approach to minimums and executed the published missed and hold. After a couple of turns in the hold; the student requested vectors to the LOC approach back to our departure airport. Because of the intermittent IMC; the student put on a view-limiting device to fully focus on the instruments while I was acting as Safety Pilot. The student executed the approach and broke out at 2000' continuing to LOC minimums at which point the student removed the VLD (View-Limiting Device) to go visual. The student was descending below the PAPI visual glide path and I mentioned that they should 'level off for a bit' to regain the glide path. At that point; the Tower Controller issued a 'low-altitude alert' and asked if we had the runway in sight which we did. The student was not regaining the optimum glide path as we had 3 reds and 1 green. I noticed the close proximity of the trees on the approach path and noted that we didn't have much clearance as the student continued for the runway with a touch down just past the REILs. The student applied significant braking to make the first taxiway. I wonder if the stress of the approach in IMC was adding pressure to the student to get on the ground and end the flight as quickly as possible. During the post flight brief I informed the student that they should make it a point to strongly adhere to the glide path information provided by the PAPI's as that will provide obstacle and terrain clearance in less-than optimal visual conditions. In reflection; as CFII or IFR Safety Pilot I should be strongly insistent in reporting flight operations any time safety is compromised.