If you are in the ZoC of the target of your Engage action, you have to move to base contact.  Whether you start there or enter during your normal move does not matter.

This is normally not a "problem" as the enemy ZoC is only 5cm, so there's no need to base them, unless you've somehow started your activation within it; this "must base" only happens with scouts' 10cm ZoC as that represents the "possible" locations of the scouting troops.  

The soldiers "on the ground" don't have the god's eye view the players do, nor do they "take turns", as the players do, nor do they stand on little rectangles like the models do.  The scouts' extended ZoC is similar to the concept of an electron probabilty cloud, the actual scouts are "somewhere in there", which is why the enemy has to react differently to them than more closely operating enemy troops.  It's an abstraction of the "unknown" location of the units for the troops on the ground.  As they move around in the "scout probability cloud", there's a high likelihood of them making dangerously close contact with the scouting elements; the game represents this by forcing you to base in this situation.

And, if you're more that 5cm away, and don't want to base, just use a "cautious move" of 5cm... simple.  Or, simply base the nearest scout with a sacrificial unit, negating its zone of control, and now you can move your other models more freely.  There are many ways to deal with the situation.