The first question always should be, what is the SWR without
Many tuners can match a length of coax that is shorted at the end. So just
because a tuner can match it doesn't mean it will be very effective - the power
is just being dissipated as heat in the coax instead of being radiated.
So let's try an example. I have a model of a 6m yagi here and the impedance
on 20m is roughly 3 - j1500 ohms. We can put that into VK1OD's transmission
line loss calculator here: http://vk1od.net/calc/tl/tllc.php
along with the feedline information and see how much power reaches the antenna.
If you have 15m of RG-213 coax then the loss in the coax is almost 28dB, so with
100W of output power you are getting less than 200 milliwatts
losses on receive will be similar, which may explain why signals seem "down" somewhat.
Now, in practice it could be better or worse than this, depending on the details of
the antenna. A beta or gamma match on the beam will have more of a mismatch
on 20m, while if one side of the element is grounded the the boom might become
part of the antenna. And, if the balun isn't effective at 20m, the outside of the
coax may contribute a lot of radiation also.
But the general rule is, just because you can match the coax with a tuner, doesn't
mean that the power is reaching the other end and being radiated. It's the SWR
on the coax between the tuner and the antenna that determines the losses, which
is not affected by the tuner settings.
A simple dipole will work much better.