There could be many explanations for this, but I'll offer a few of the more likely ones.
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It may simply be that your loop is not a 50 ohm match, and when tuned for "maximum smoke", the actual input impedance is something other than 50 ohms.
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The Alextune is basically a simple RF "sniffer", and the nearby E-Field energises a LED, which glows more brightly as the RF field strength increases.
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I think the W2LI magnetic loop antenna is a slightly different design to the Alex loop, in that it uses two capacitors in what is often called a "Navy Match" and it doesn't use a separate feed loop.
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As a result, the RF field around the tuning box may not be entirely produced by radiation from the loop itself, and some of it may be from the internal wiring. Therefore, the localised E-Field, where the Alextune is attached, may not correspond to maximum radiation in the far field. I note that some versions of the W2LI magnetic loop also have an extra external balun box, which also suggests that here may be some unwanted feeder radiation too, which is not uncommon with many commercial loops. This will also distort the local E-Field around the antenna.
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If you are feeding the loop via a length of coax. The SWR you observe at the radio end, may not be the same as the SWR at the interface between the coax and the loop. If you tune the loop for best match at the radio end, it may well be something different at the loop, but as long as the radio is happy with the match, the SWR protection shouldn't kick in, and the radio should be producing it's maximum output power. However, modern transmitters don't have a 50 ohm output impedance, but they are designed to deliver as much power as possible to a 50 ohm load, as long as the output voltage and current don't exceed the rated limits of the PA devices. As a result, they can sometimes be "fooled" into producing more output into something that is not an exact 50 ohm resistive load, but one has some reactance present.
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I hope this helps.
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Martin
