the amp needs to be on in order to see the input tune.
with the amp off, you are seeing the SWR of the antenna, as the amp relay contacts are just passing the signal right through the amp.
first, just because of the way you worded things, i want to make sure you're not saying that you are using the SWR meter itself as some sort of "tuner".
to see how well you're amp's input tuning is matched to your radio, you can use the radio's internal SWR meter, or if the radio doesn't have one, you can put an SWR meter in between the radio and the amp temporarily.
now with the amp on, and an antenna or dummy load connected to the output of the amp, key the mic, calibrate the SWR meter, switch it to read SWR, and note the value shown. It should be less than 2:1 and preferably 1.5:1 or better.
now to see how well the output of your amp is matched to your antenna, put the SWR meter between the amp and the antenna, and repeat the test. amp on of course.
LC
