How do the two half cells of Daniel cell know when they are connected?
No, electrodes do not know about each other.

When an electrode is inserted to an electrolyte, the electrochemical reaction is ongoing in both directions. If reduction direction overruns oxidation, the potential of the electrode is increasing ( or vice versa ) until the rate of both reaction gets equal, the net reaction rate is zero and the electrode reaches the equilibrium potential.

That may be quick or slow, depending on the electrode and respective reaction kinetics.

When both electrodes are galvanically connected, the electron exchange due the potential difference disbalances the equilibrium potentials of both electrodes and the net electrochemical reactions get the steady non zero rate.

Note that the electrode potential is conventionally referred to the Standard hydrogen electrode (SHE), which itself has potential $\pu{+4.44 \pm 0.02 V}$ ( Wikipedia ) wrt the potential of a free electron in vacuum. So saying $\ce{Zn}$ electrode potential is negative rather means it is less positive.



You may want to try searching various terms in wikipedia and following relevant internal/external links. The great source of compactly explaned topics is hyperphysics, but with limited scope. It is a kind of hyperlinked quick cards/cheat sheets, very handy, if you want to understand the basics.  This link is particularly for Electrochemistry