Of course not. As already mentioned in the comments, homoclinic tangle is considered for maps, usually derived by taking a Poincare section in phase space of continuous systems. For example, consider a continuous systems with hyperbolic periodic orbit with period T in $R^3$ (or equivalently, consider a non-autonomous continuous system in $R^2$). Then the time-T map of this system, which will be map $P:R^2\rightarrow R^2$, you may see a homoclinic tangle. This is exactly what is done in the notes that you mention (since the second term in eq. 2.2 is time-dependent). Once you have time-dependence, you are really working in one higher dimension that the dimension of $x$. Hence, the tangles are NOT intersecting in the full 2 (for x)+1 (for time) dimensional space, but rather in a 'collapsed' 2D space, in which time dimension has been collapsed. It is like looking from above on to the x-y plane if time is Z axis.
"Deterministic law" as mentioned in original question, is nothing but uniqueness of solution of the system of ODEs under consideration. If the r.h.s is Lipschitz (or even better differentiable/smooth), it is guaranteed to have uniqueness. And we surely get tangles for many smooth systems.