The following applies to SM G900T phone running 5.1.1 FOL1, using another carrier, Ultra Mobile, and its Sim, NOT T-MOBILE. Phone has root.
As most know, trying to use the Mobile Hotspot from the T-Mobile firmware Modem meant that the phone would check if a hotspot had been subscribed to for T-Mobile or any other carrier.
If no subscription, the Mobile Hotspot would not work.
Since the phone was no longer using T-Mobile service and had root, deleted the T-Mobile account and two other T-Mobile labeled apps, (which also saves on battery usage).
Now, when I try to use Mobile Hotspot, which remained along with the T-Mobile logo, it says checking (verifying) (with who or if is anybody's guess, but its not connecting to T-Mobile) and then the hotspot is allowed to work.
It works great.
If I switch back and forth for comparison with another phone and using WiFi Tether Router 6.08, one or the other hotspots may not work. Apparently, they interfere with each other.
Simply cleared both phones using Root Cleaner, rebooted both phones, and either hotspot works again.
So far after some testing, prefer Mobile Hotspot. It is FASTER and can be configured to only connect to a device if you input the mac address (one time only), this seems a little safer than WiFi Tether Router, which also works well and will be kept just in case.
WiFi Tether Router worked without any needed changes in configuration.
Its settings, either by default or self adjustment, match what others have recommended in earlier posts here.
Mobile Hotspot as explained, required the removal of 3 T-Mobile apps and one configuration change in the APN.
APN protocol from IPv4 to IPv4/IPv6.
That solved a limited connection to a laptop.
Hope this is of some help.