"was" is past, so continue on with that tense:
"... was being chased by another dog when it suddenly decided to dash across the road. I watched everything in horror as my heart twinged for what I'd just witnessed."
Note, "I'd" is a contraction of I had (past tense).
About "dash", it's part of the to-infintive "to dash". Infinitive verbs do not carry tense.