Either can be correct in the right context.
You were the person who killed their mother, and you still are the person who killed their mother.
"Who killed my mom?"
→ It was I who killed killed your mom.
"Who is the person who killed my mom?"
→ It is I who killed your mom.
Having said that, if there is no such exchange of dialogue to set the context, and each sentence is being offered as an unsolicited statement, then the past-tense version would be much more likely to make sense.
The present-tense version is jarring on its own, because the murder happened in the past. So, as a simple utterance, the past tense better matches the past event.
Using it is I only makes sense in response to a previous present-tense question that sets the stage, so to speak, for a present-tense reply. In fact, it would actually be jarring to hear a past-tense reply to a present-tense question.
If the statement is a reply to a question, then whichever tense the question is asked in would normally be the tense that it's answered in.