Unless the wiki is mistaken, the Tigershark is supposed to be passive unless you stray close to its den. And it is, with Wendy... but it will chase Abigail to the ends of the Earth.
Not sure if this is necessary in the bug forum, but *spoiler alert*.
In a hilarious happenstance (you know, taking things in stride), my first encounter with the Tigershark on land came with absolutely no warning when it leaped up on shore out of nowhere and started trashing my sandbags. I had encountered it at sea a half dozen times or so, which was quite frightening. Watching it prance ashore and lay waste to my base like a cat with a ball of yarn was a delightful spectacle. However, usually these boss encounters have a bit of forewarning. If I'm not mistaken about it's den location (does it appear as a sand hill with a shape somewhere between a pyramid and a fin in other seasons?), it was on the other side of the map and I hadn't even ventured close for days.
Then it showed up again in another game, right when I needed Abigail to hunt some wereboars. That's when I confirmed that she wasn't hostile to Wendy, because after finishing off Abigail, the Tigershark just stood there. In that game, I hadn't even seen the den.
I would wager that if you play as Wendy and keep Abigail around, you have a 60-80% chance of encountering the Tigershark at least once during the monsoon season, particularly if you leave your base island for almost any reason.