There is nothing wrong with a "cheapo" table if it fits your needs. The following is from Wood Magazine about router speed:
Routers with variable-speed motors run between 8,000 and 26,000 rpm. More important than speed at the bit shank, though, is a bit's rim speed, the velocity of the cutter at the farthest point from the center of the shank. For example, a 1⁄2 "-diameter bit spinning at 10,000 rpm runs almost 15 mph at the tip of the cutter. Increase the speed to 25,000 rpm and the bit's rim is traveling at 37 mph. Now take a 3"-diameter raised-panel bit. At 10,000 rpm the rim travels nearly 90 mph, but at 25,000 rpm the rim speed would capture the pole at any NASCAR race: 223 mph!
Speeds greater than 100 mph put excessive stress on bits, especially those with 1⁄4 " shanks, and increase vibration. In addition, cutting performance suffers, as shown below, when speed exceeds the optimum level. Routing at a too-fast speed causes tear-out and burn marks on the workpiece and dulls bits faster. Routing with the speed set too slow leads to choppy, rough, or rippled cuts.
I use the Frued adjustable bits for rail and stile. The bits make a lot of noise so wear hearing protection. If you are getting excessive vibration from the whole router table then screw some boards on the bottom of the router table and then clamp it down. You should be clamping it down anyway. With the table being rather lightweight, a spinning large bit and depending on your feed rate you have a lot of moving parts to cause problems.
If the bits are not loosening the screw that holds the cutters together then it is just the combination of your router table vibration, router speed and router bit rotation.
Run some material through and check it out to see if you are too fast, too slow, or just right by looking at the finished piece. Using a 1`.5" spinning bit I would set the router speed to about half speed. Every router runs at different speeds. After running a test through then increase or decrease the speed a little. Since most people run 1/8" to 3" bits, the 1/8" runs at top speed and the 3" at lowest speed then it makes sense that 1.5" half speed + or - a few RPM.
One rule of thumb is that you never remove more material in one pass than your router bit cutter diameter. So in your case the tongue is 1/4" wide and maybe a 1/2" deep. So only remove 1/4" depth at a time by moving your fence and making multiple passes. So be sure to mark each board with the top so you always run it the same way. It is almost impossible to get a board perfectly centered and if you run one side up on the first pass then turn it over on the second pass you will have a grove that is bigger than 1/4" and an uneven bottom.
To set up the fence use a straight edge on the bearing and line up the fence with the bearing. Then mark your table and move the fence forward and make a pass on all material. Then move the fence back once or twice till you get to the marked line or just use the straight edge to line up the bearing and fence.
This will make a better outcome then trying to run it all at once for the full depth.
Also look at the grain direction. Some wood like oak are very easy to chip out. It is like petting a cat. If you pet from head to tail the fur is smooth and the cat purrs. If you pet the cat tail to head the fur is ruffled and the cat tries to scratch you. So look at grain direction and try to cut down hill, when you cut up hill you get tearout, chipout and generally rough finish.
Good luck and let us know what worked and what did not work.