Spurious triggering in TRIAC due to EFT
You are not &quot;worng&quot;. It is most likely that either the opto-triac or, more likely, the BTA16 is being triggered by a transient from the other electrical device being switched on an off.
Triacs are normally turned on by triggering the gate, as in your schematic. They can also be turned on by high \$\frac {dV}{dt}\$ across their terminals and the transient could supply that. The datasheet lists in its features

High Immunity to dV/dt - 1500 V/μs minimum at 125°C. (Page 1.)
Minimizes Snubber Networks for Protection

Despite the snubber comment it looks like you need one. A simple RC type would suffice. Make sure it's rated for your mains voltage. (i.e., Don't expect a DC capacitor to last very long!)