I assume they play to win while putting X and Os:
Jill is supposed to win
Jill has started to put X first as shown below.
The reason is
If O was started to play, he would have won already after the third move whatever Jill played to block or win.
To explain it more:
In the example above, if Jack would have started to play on this corner, whereever Jill puts his X, Jack would put his O in the yellow part and would have forced Jill to put her X on the right hand side of the board so it is impossible.
Let's assume Jack put his O in the middle first, his second move cannot be the yellow one as explained before, so his next move could only be Green square.
For the green sqaure:
After Jack puts his O to the green square (3,2), Jill will have to put her X to (1,2) if she did not put it already, but it does not matter. If she already put it there, Jill's next move will have to be (2,1) not to force Jack to put his O to the (1,3). So after that, Jack would put his O to (3,1) and this will force Jill to put his X to (1,3) or (3,3) which was not the case. I will not explain the third possibility since it is very obvious.
So the play could be like below and for sure
Jill won this game as the next player would be her.