To me I still don't understand how that "tee" works. So when sewer water backsup, isn't it still going up both pipes at the "tee" intersection?
Sewer water would backup both pipes through the 'T' but the height of the lower pipe opening, establishes the maximum height any fluid could back-up. As sewer fluid will be released onto the floor out of the lower pipe opening, it cannot then continue to back-up the taller stand pipe to the filter/softener drain tubes. This assumes the clear drain tubes do not extend too far into the standpipe. The open ends of the drain tubes need to remain at least 1" above the height of the lower drain pipe opening.
Since the air gap 'relief opening' is not within the standpipe itself, I can understand Reach4's comment that it may not be in compliance with code. As there is probably little risk that either the standpipe or the 'T' would ever be blocked, it appears this configuration will be reasonably effective to prevent cross contamination.
As mentioned, a 'P' trap is not shown. As you were lead to believe that the drain is routed into the washing machine standpipe and the trap is located there, it would be good to verify. You could post a photo if possible.
I see that the brine tank overflow tube continues to be routed uphill into the standpipe. Since a brine tank overflow is unlikely, it probably is a none issue.