There is another way of looking at quaternions - they are identical to matrices of a certain kind. Quaternions of the form $bi + cj + dk + a$ can be represented by matrices of the form
$$
\begin{bmatrix}
a+bi & c+di \\
-c+di & a-bi
\end{bmatrix}
$$
where the $i$ inside the matrix is $\sqrt{-1}$.
The matrix representing the quaternion $i$ is
$$
\begin{bmatrix}
i & 0 \\
0 & -i
\end{bmatrix}
$$
Write down $jk$ in this form
$$
jk=
\begin{bmatrix}
0 & 1 \\
-1 & 0
\end{bmatrix}
\begin{bmatrix}
0 & i \\
i & 0
\end{bmatrix}
=
\begin{bmatrix}
i & 0 \\
0 & -i
\end{bmatrix}
$$
which is clearly $i$, not $-i$.
The rule is do nothing with quaternions that you cannot do with matrices of the form given above and you'll be ok.
Edited to add: If you think of $(jk)^2$ in terms of matrix multiplication,
$$(jk)^2=jkjk=ii=
\begin{bmatrix}
i & 0 \\
0 & -i
\end{bmatrix}
\begin{bmatrix}
i & 0 \\
0 & -i
\end{bmatrix}
=
\begin{bmatrix}
-1 & 0 \\
0 & -1
\end{bmatrix}
=-1
$$
But $j^2k^2$ = $jjkk = jik = $
$$
\begin{bmatrix}
0 & 1 \\
-1 & 0
\end{bmatrix}
\begin{bmatrix}
i & 0 \\
0 & -i
\end{bmatrix}
\begin{bmatrix}
0 & i \\
i & 0
\end{bmatrix}
=
\begin{bmatrix}
1 & 0 \\
0 & 1
\end{bmatrix}
=1
$$
