‌ to your second question: I've been working on SharePoint everyday for 8 years now (2003, 2007, 2010, 2013, Online where does the time go!?), so if we're talking about pure SharePoint then yes it's a Choice column and not a Lookup column.  We went with Choice in this scenario to try and keep things simple and avoid lookups.

In the Nintex Form the control is also called a "Choice" form control and is connected to the SharePoint on-prem choice column.

Marian Hatala‌ to your third question: I did try creating a calc value control with formula set just to 'namedControlChoiceName' to proof check how it actually evaluates, and it seemed to always be blank in the Nintex Mobile Phone Layout on Android with the calculated value formula set to a named control directly.

I also tried with a variable set to a named control, and then the variable attached to the calculated value control, just to try to double check.  But that wasn't working.

I tried again today using a different named control attached to a choice column, and the formatting rule seems to be working now as expected...(to my chagrin)...

Hypothesis 1: The Name of the Control and the Connected to column must match for this to work?

Hypothesis 2: I am just testing/changing too quickly and there's some setting that I keep missing to gain consistency...

This works with a simple single line of text string:

This also works (to my chagrin):

I think my hypothesis 1 may be true... I think it may be important for the Name of the Control to be "My Pretty Name" and the Connected to value to be "MyPrettyName"!  It's also still possible that my hypothesis 2 is also true 

Case closed, thanks for talking me off the ledge 

Also the reason I've been trying to avoid renaming Controls in the Form is because they get really hard to recognize in the Formula Builder for Rules.  It's not terrible for this project because I only have 2 layouts and a dozen columns, but I could see it getting trickier for bigger forms.  I have habits built up for quirks like this in InfoPath, I guess it's just a matter of getting a good habit developed for this on this platform Vadim Tabakman Emily Billing 

I've been working on SharePoint everyday for 8 years now (2003, 2007, 2010, 2013, Online where does the time go!?), so if we're talking about pure SharePoint then yes it's a Choice column and not a Lookup column.

sorry I've asked, but people sometimes do not recognize the difference.

so I learnt rather to clarify at very beginning then exchange 20 or so posts to find out specification was wrong.

from your screenshot I see you use site (choice) column,  that is some specific what I don't see you would mention it.

since I do not use  site columns so often I set up a testcase for choice column, for me it works correctly

Hypothesis 1: The Name of the Control and the Connected to column must match for this to work?

I've never experienced anything like that (for any control), and I wouldn't see it as likely reason.

in my above example list field name and control name were completely different for both type of columns.

just curious, have you renamed that choice site column after creation, ie. does display and internal names differ?

Hypothesis 2: I am just testing/changing too quickly and there's some setting that I keep missing to gain consistency...

not sure what you mean with 'too fast'

hopefully, you test with published form, not just with preview - preview is preview, not everything need to work or work reliably.

to test on mobile device, it's always good to invoke manual refresh first

This works with a simple single line of text string:

This also works (to my chagrin):

I' not sure I get what you wanted to show with these two screenshots.

for 1st screenshot, I understand it: if 'IncidentNumber' single line text  control contains digit '1' then rule works correctly. so far quite good

for second one, what is 'MitigationSuccess'?

it's first time I see it in your posts. so I hardly can guess what should it do or how can it behave...

is it named control connected to 'Task outcome' list field?

I think my hypothesis 1 may be true... I think it may be important for the Name of the Control to be "My Pretty Name" and the Connected to value to be "MyPrettyName"!

as explained above, I don't think this is proper explanation for what you experience.

for 'control name' you can type in whatever you like. internally form control is anyway identified by a GUID.

for connected to field, you are provided with list of possible values. so (if there is not a bug in application) you can not any not valid value here.

they get really hard to recognize in the Formula Builder for Rules.

yes it's good practice to distinguish list item's filed names and form control's names, resp. in general duplicated names for different objects.

see What's in a name? 

I tried again today using a different named control attached to a choice column, and the formatting rule seems to be working now as expected...(to my chagrin)...

 ...

Case closed, thanks for talking me off the ledge 

so, have you got resolved your issue?

from your several posts within short period of time I'm not sure at all.