Does Alcatel One Touch Idol 3 show which LTE Band is used (e.g. 12)?
I currently have the Alcatel OneTouch Idol 3, and yes it does support band 12. In fact, my phone is currently using band 12 over band 4 which is what my OnePlus One was using, since it doesn't support band 12. 


One way to check is to download the LTE Discovery app. 
Or, open your phone's dialer and type *#*#4636#*#* -- this will open up Testing mode.


Go to Phone information and it will show which band your phone is using.  
See screenshots below. First two are from my Alcatel OneTouch Idol 3 and the last two are from my OnePlus One. As you can see, the Phone information mode for the OnePlus One does not show the LTE band for some reason. (Depends on the phone I guess.)

Also notice how band 4 is in use on the OnePlus One according to LTE Discovery and there are no bars, whereas the Idol 3 has 2 bars of Band 12 LTE. 



Note that these two phones are placed right next to each other.







Click image(s) for larger version