If multiple fluid providers with the same fluid are on a network, fluid supplier pipes will draw only from the nearest provider, even if that provider is insufficient to provide the full amount required.
For example:

This setup will fill the three Resonant Tanks to 250 buckets capacity in about 20 seconds (give or take a few seconds). Each source tank fills one destination tank.

Paradoxically, however, connecting the three parallel routes will increase the time it takes the tanks to fill, to about 45 seconds- the center, closest source tank will fill one destination tank, then the next, then the next, and the two on the sides will not contribute.

If the tanks are replaced with chests and the fluid pipes with their regular equivalents, the system demonstrates a more sensible behavior and uses all three source inventories to fill all three destinations whether or not they are connected.

I have been able to get more than one provider to work at once, but not reliably, and so I don't know what to do to reproduce that effect.

Minecraft 1.12.2
Logisticspipes 10.4.21

I can confirm this behavior.
My plant consists of 2 high pressure boilers for steam generation, as shown in the following screenshot.

1 boiler can easily keep up with 2 steam turbines.

The first piperouting was a single pipe in the middle between the boilers - which didn't work because only the porvider on the right side was sending to the fulid supplier and the left boiler was completely ignored.

Therefore, the speed of the only "seen" boiler was not sufficient to supply steam to the 4 steam turbines of the railcars via a central pipe.

Therefore I changed to 4 suppliers with dedicated pipes (2 per tank) and 4 turbines as shown on the screenshot.

Playing on MP
forge-1.12.2-14.23.5.2860.jar
railcraft-12.0.0.jar
logisticspipes-0.10.4.18.jar
openjdk version "1.8.0_342"
OpenJDK Runtime Environment (build 1.8.0_342-8u342-b07-0ubuntu1~20.04-b07)
OpenJDK 64-Bit Server VM (build 25.342-b07, mixed mode)