As other's have said, the tip-off itself won't trigger pirates unless the mission you had the tip-off for is still active.
I had one the other day where I was at the nav beacon for the system and I just had pirate after pirate saying the whole "you got something I want" line despite my hold being empty. Think I killed about 6 before I got bored and left, kinda helped that since being at the nav beacon, system security were also present.
I also had 2 random interdiction attempts recently (first since playing, over 300 hours on this account presently) 1 was by system security, despite me having no bounty, fines or illegal cargo/passengers, and the other was from a random pirate telling me he wanted what was in my hold, despite not only being empty, but also having no missions.
So basically, this kinda stuff does happen randomly sometimes, but unless you have cargo/missions where "ships may be sent after you" is in the description, it's far less likely.