I'm using a MoCa spliter left behind by the previous Direct TV service I had.
Worse, they ARE optimized for DirecTV's MoCA (DECA), which means they have lower output port-to-port isolation in the DirecTV MoCA (MoCA E-band) frequency range, 400-700 MHz (bad for your TV signals) and higher port-to-port isolation at satellite TV frequencies, 950-2150 MHz (very bad for CATV MoCA, i.e. MoCA D-band).As already noted the standard green label Directv splitters are not optimized for MoCA on CATV. DECA which is Directv's version of MoCA uses the frequencies 500-800MHz normally used by CATV, which is why you can't mix DECA with CATV and why you can't use MoCA(1100-1675MHz) with Directv.
So, you *will* want to replace the DirecTV splitter with a MoCA 2.0-compliant splitter per fcfc2's recommendation above (avoiding the 2 models labeled "DirecTV," as stated). It's difficult to provide a more specific recommendation, not knowing where your cable modem is located. Generally, you wouldn't want a single 4-way split as the current setup appears to have; instead, you'd want to deliver the best possible source signal to your modem and CATV tuner (i.e. the BOLT), with priority usually going to the modem. The MoCA-only feeds can be hung from a secondary splitter.
As for the "PoE" MoCA filter, you'll definitely want to get one installed. It's not just to keep your signals secured within your home, but to improve MoCA performance by reflecting the MoCA signal back onto the lines. In fact, if you were to have one on that DirecTV SWM splitter, it might help overcome the high port-to-port isolation -- though you'd *still* want to replace that splitter.