There are two ways of doing this.
You can isolate the MPU from the triac gate/MT1 (e.g. using an optoisolator) and then you can connect the MPU to any potential you like or even let it floating. This simplifies any MPU input signal processing, since you can connect the MPU Gnd to the signal source potential.
The other option is that the MPU board is directly connected to gate/MT1, in which case the MPU signals are close to the MT1 potential. Please remember, that if the triac is powered through an unpolarized mains plug, there is a 50 % chance that the gate/MT1 and hence MPU input terminals are sitting on top of the mains voltage and hence the input terminals can be momentarily 300-400 V above any grounded objects. Thus each input must be separately isolated to prevent any mains voltage from harming any people, depending on which way the mains plug is inserted.
If there are many inputs that needs to isolated, it is easier to put a single isolation barrier between the MPU and triac and using direct connections to the MPU input pins rather than isolating each input separately, when directly connected to the triac. However, as long as all the inputs are from potentiometers with isolated knobs, well isolated mechanical switched or an IR receiver, the MPU could as well be directly connected and possibly sitting on the Live potential,
With the 2N6071 triac referenced in this tread, when using direct connection, it might be better to connect the MPU Vcc directly to MT1 and MPU Gnd to -5 V relative to Neutral.
In the old days, tube TVs, at least in Europe, had a single rectifier diode from one mains plug pin to form about +200 V anode voltage and the other mains pin was connected directly to the chassis. Depending on which way the mains plug was inserted, the chassis had either Neutral or Live 220 V connected to the chassis. Thus it was very important to use a isolating wooden box as well isolated knobs on all potentiometers and switches. Any electrical connections were very rare, however, adding an external speaker connection was easy, since the audio output pentodes required an audio transformer anyway, which isolated the speaker terminals from mains and potentially from direct Live connection.
When servicing such TVs and other devices with universal (AC/DC) power supply, the first thing was to check which way the plug was inserted in order to avoid having 220 V mains all over in the chassis and getting nasty shocks from it.
Current regulations require that when servicing such beasts that an isolation transformer must be used, so that when touching the chassis, the chassis potential will be the same as your potential.
These days when using MPU controlled systems controlling directly a triac and hence sitting with 50 % likelihood directly on the Live line that an isolator transformer should be used, when developing and servicing such systems, if they are connected by an unpolarized plug to the mains.
Paul