Mine does the same thing on start up it's probably mode switching at first and once it's fired up it settles down. I think this is normal for these pen type lasers and as long as it dosen't stay in TEM01 then all seems to ok with it.
It's normal to have some "warm up" variation in DPSS lasers. Thermal changes in the crystal set can cause variations. Mode switching during warmup is common, and there are other factors too. The specifications and temperature of the components plays a part.
The wavelength of laser diodes is not dead on - that is, straight from the factory, some will produce slightly higher or lower wavelengths. The wavelength of the diode changes slightly as it warms up. On the other hand, the range of wavelengths that the lasing crystal will operate on is very narrow - and it is also affected somewhat by temperature changes.
When you turn the laser on and the diode warms up, if it's wavelength is approaching that of the lasing crystal, you will see a power increase, and if the wavelength is receding, you will see a power decrease. The ideal case occurs when the wavelengths coincide at the same time that everything reaches optimum temperature and condition.