when using a test indicator
1) attach test indicator with shorter bracket , rods for more rigid and repeatable setup. if you can move test indicator bracket too easily, pushing on it with 1 finger it may not be rigid enough for precision work.
2) all machines move under load. a machinist turning a dial can easily put enough force to move table around just by lean on it with his weight. even a feed motor can move the table under load. try tightening table gib or slide locks. many machinist leave all slide locks 1/2 tight always for a more consistent and accurate machine performance.