The following is direct from the O.S. Max .46 LA owner's manual:

"All internal-combustion engines benefit, to some degree, from extra care when they are run for the first few times - known as running-in or breaking-in. This is because the working parts of a new engine take a little time to settle down after being subjected to high temperatures and stresses. However, because O.S. engines are made with the aid of the finest modern precision machinery and from the best and most suitable materials, only a very short and simple running-in procedure is required and can be carried out with the
engine installed in the model.

The process is as follows:

1) Start the engine and, with the throttle fully open, open the needle-valve an extra half turn (180°) from the optimum setting. This will produce a rich mixture that will result in cooler running. Allow the engine to run out a full tank on the ground. (Avoid dusty surroundings.)

2) Now fly the model with the needle-valve re-set 20-30 degrees open from the optimum setting ( i.e. 40-60° from the highest rpm setting ).

3) Close the needle-valve very slightly on successive flights so that the engine is running on its optimum needle setting at the fifth or sixth flight."

Basically, your flight instructor set your trainer engine rich of peak power as described in step 1. Per the manual, one tank of fuel run on the ground would be best. Running that same tank through in the air won't hurt anything so long as the needle is set a 1/2 turn rich of peak rpm

alfredbmor and your flight instructor were both right. You need to follow the manufacturer's recommended break-in proceedure for whichever engine you're breaking in. Your instructor did that simply by tuning the engine to run a bit rich for the first few flights. alfredbmor is correct in pointing out that most engines can't just be fired up and flown quite like the O.S. Max LA-series engines.

Again, your .46 LA is fine. Be sure to read the instruction manual for the break-in proceedures for future engine purchases, however, as not all glow engines are quite so flexible.