There were two main reasons that Shingi decided to join the fight, not Wild Tycoon. First, Jathurth's attack power had increased more than he had calculated, which was way over what Wild Tycoon could handle. Before, she could last up to five attacks, but now she could at most two.
The second reason was that the HP aura of Jathurth was at a point to be low enough that they had a chance to win this in time. He still wasn't sure of the specific number, but by his calculations, Jathurth should be at 40% of his HP.
Taking part in the battle had disadvantages since it increased the chance of him getting hit, and he could lose his focus on his active Spells. But, of course, that meant he had to increase his focus on defense and had STONESKIN on him, trying to lessen at least hits he couldn't avoid.