Display configuration problems with Mac Pro
Solution 1:
Remember that this model of Mac Pro came out in 2013, 4K/60Hz came to DisplayPort 1.2 in 2010, and 4K/60Hz came to HDMI 2.0 in 2013. HDMI 1.4, which is supported on this model, supports 4K video at only 30Hz. It looks like there were updates to the operating system and drivers that added some more support for 4K displays but that doesn't change the hardware behind the HDMI port the computer has, or any other hardware limits on HDMI 2.0 support.
Passive DP to HDMI cables and adapters will simply advertise to the GPU that it can speak HDMI up to version 2.0 and assuming the GPU supports it that's what it will get, and this will give 4K at 60Hz. Active DP to HDMI cables and adapters advertise themselves as a DP device to the GPU and do the HDMI conversion itself, meaning the video source can support an older version of DP to get 4K/60Hz.
This model of Mac Pro will support three 4K HDMI displays but not at 60Hz, for that you need DisplayPort. To get 4K/60HZ to your HDMI display mean you need to make it look like a DP display to the GPU.
My best guess is that you are using passive DP to HDMI cables. Passive cables will require a video source that supports DisplayPort 1.3 to get HDMI 2.0 signals out of it. And DisplayPort 1.3 was not published until 2014.
Perhaps an active adapter like this would work: https://www.startech.com/AV/display-and-video-adapters/Displayport-Adapters/mdp-hdmi-2-adapter-4k~MDP2HD4K60S
I have not tried this adapter myself, your milage may vary. Not a paid endorsement of StarTech, just a happy customer.
Solution 2:
Apparently, there are three buses on the Mac Pro, which can handle either two normal (p.e. Full HD) displays or one 4k display.
[1] [2]
[1] [2]
[0] [0]
The numbers indicate to which bus those ports are connected. Moreover, the Mac Pro has got an HDMI output, which is also connected to bus 0. Apparently however, if you want to get three 4K displays to work, you have to plug one of them into a port from bus 1, one into a port from bus 2 and one directly into the HDMI-port for some reason. (I assume that this will not be a problem as you are using Thunderbolt to HDMI adapters anyway)
For more detailed information, please take a look at: How do I connect a 3rd 4K monitor to my 2013 Mac Pro?
Good luck!