Should Water Sediment Filters Come Before or After Water Softener?
I'd prefilter (based on your other question calling this "ridiculously rusty water") ahead of your replaceable cartridge filters with a cleanable/dumpable screen filter (a vortex with a permanent screen in the middle and a catch chamber and dump valve on the bottom) between the pump and the pressure tank. That type of filter works best with fast flow.

In fact, I do on my own system. Put a bucket under the valve and it removes what's caught in the chamber and blows the screen clear (since the pressure tank is on the "clean" side of it.) 

The cartridge filters will be better on the upstream side of the pressure tank (where they are now) since faster flow does not help them work better.

As for the plumber, sounds like "future plumbing work guaranteed" to me. So the plumber might like it that way - having fought a water softener with valves that got funky in a "rusty water house" I'm not in favor of dumping rusty water into one unfiltered.

Edit - if you WANT to rearrange your filters you could make some small argument for putting the activated carbon (taste and odor) after the softener, but it's a small argument and probably not worth the hassle. You might want to take off the "watering gardens" water before it and the softener, though.

This is the type of filter I use - "spin-down" or "vortex" or "sediment trapper" with a sediment trap below the actual filter screen. water enters and is spun around the outside at high speed, then drawn through the screen - a fair bit of the junk slides down the walls where it's thrown &amp; falls into the trap and thus is not clogging the screen. 

I use the 200 mesh (finest) stainless steel element, as I'm dubious about the longevity of polyester screen elements, which go finer. And I very specifically put it between the pump and pressure tank, which is not where the manufacturer suggests, but it makes the best engineering sense (since having the tank upstream means that dumping the sediment trap automatically backwashes the filter, &amp; it does not have to be opened in normal circumstances.) If the water shed is not dark you might want to give it a box or a black bag over it to keep it from growing algae. Look occasionally and dump what it's caught.