I can't talk to JRemote for iOS as I no longer use Apple products. Perhaps if you stick to using the laptop as a MC Client to try to work out what is happening. If this problem doesn't happen using the laptop, it could be an issue with JRemote for iOS, and someone else will have to step in. Or you might find a setting in JRemote around adding files to Playing Now versus replacing files, and shuffle, etc.
iTunes works very differently to MC. I think what's happening is just a result of the way you are using MC. I tested using the "Audio -- 100 Random Songs" Smartlist various ways, and it is working fine.
MC has:
Playlists, which are sequenced static lists of tracks.
Smartlists, which are sorted dynamic lists of tracks populated by rules.
Playing Now, which is like a Playlist, but is created when tracks are played, or tracks, or Playlists, or Smartlists are added to it. Playing Now is much like a Playlist, but it is what MC plays. MC doesn't play Playlists or Smartlists, it just copies them to Playing Now, and either starts playing them immediately, or doesn't, depending on settings.
All three, Playlists, Smartlists, and Playing Now, can be shuffled. In Playlists and Playing Now you can also drag and drop files, to add or resequence tracks (note the "Seq" Sequence column on the left), or click column headers to re-sort them. Also in Playlists and Playing Now you can save that new sequence with the "Update Order" function. You can re-sort Smartlists but they don't have a defined sequence, and the content is defined by its rules.
Check all the settings in "Options > General > Behaviour" and "Advanced".
There are settings that define what happens when you add play something or add something to Playing Now. In your situation, it sounds like Playing Now had a whole lot of stuff in it, and then you played the Smartlist, which added to the existing content and shuffle the tracks.
Check that Playing Now is empty before you play the Smartlists. If you don't "Clear Playing Now on exit", then add a Smartlist to Playing Now, and have "Start playing when files added to Playing Now" set, plus Shuffle turned on, then you could get what you are observing.
There are also multiple ways of starting playback, via the right-click menus on many parts of MC. So even if you don't have Start playing when files added to Playing Now" set, you could right-click a Smartlist, Playlist, or Album, and select "More Play Options > Add (play now)" and see what you are seeing. Check out the other right-click menu options, like Send-To.
Explore all of the above, learn, and enjoy!
Oh, plus read the Wiki.
https://wiki.jriver.com/index.php/Playlistshttps://wiki.jriver.com/index.php/Smartlistshttps://wiki.jriver.com/index.php/Playing_Nowetc.