The specs say it has up to 1.5 % (in)stability at some frequencies. That would be +/- 30 Hz at your 2000 Hz. Your 1990 Hz to 2010 Hz are well within the specs. So you got what they promised. Not that I would have bought something with +/- 1.5 % stability, but they were at least honest upfront.
If this happened right after you turned the instrument on then there is hope that it gets better. Instruments like these need to be "warmed up" before they reach their most stable operating conditions. This typically means to have the instrument running for at least an hour. I know instruments where the manufacturer even requires four hours warm up to reach the guaranteed specs. Some people therefore never even turn of instruments.
However, the whole instrument as such looks like typical last decade Chinese design, copied from some western design from the '70 or '80 of the last millenium, re-badged for Madell. The OEM is likely Yang Zhong Ketai Electronic Instrument Co.,Ltd, alias Yang Zhong City Light and Electronic Instrument Factory, alias Micaltek, alias Caltek, alias Y-Caltek. As you see from the many names, we are deep down in the Chinese OEM naming game. And, of course, they have "tek" in some of their names in the hope that some of the reputation of Tektronix would rube off.
This is your generator in its natural habitat:
http://www.y-caltek.com/cn/products/generator.htmIt is an outdated design, although designs like this are still sold by many, usual Chinese, manufacturers. Typically the stuff is robust but not very accurate. $250 is IMHO OK for such a generator, but not a bargain.
BTW: If you want to learn, then one of the things to learn is that it is Hz and kHz, not hz and khz. Sloppy notation will bring you into trouble sooner or later.