The Essentia Input Hatch does not accept essentia whether I hook it up through thaumcraft's tubes or the essentia transfuser.
The Essentia transfuser is supposed to take essentia from jars and place it into any machines that need it. i'm not super familiar with how it works so it could be my lack of thaumcraft knowledge but I expect the machine to take the essentia in.

I set up a simple recipe that takes coal and aer essentia and turns it into a diamond. JEI does recognize the recipe as valid.

Recipe in JEI:

I have tried using tubes too.
Again, I'm not super familiar with Thaumcraft so I could be doing something wrong.

I have test it too. But with an older version (1.4).
Didn't work.

For problems with low suction, Use essentia buffers with arcane bellows. Adding the bellows will increase the suction of the buffer, and shift right clicking the piece of pipe going out of it (the one conected to the modular machine) until a blu band appears will treat that side as if it had only 1 suction, so the essentia the buffer is taking in will go out trough it,(since 1 is less than the input block's 32).

After some more testing, it seems you can right-click phials onto the input for 10 at a time. This IMO is not ideal though as it makes automation difficult and also if the pack dev decides to use a number not divisible by 10 I don't know how the input hatch will behave. Also after testing, a jar has a suction value of 63 whereas the input hatch has 32 untyped.