Ticks operate on 0.6 second cycles. So you can click at the 0.5 second mark and then move the next 0.1 second, or click at the start of a tick (0.0s) and wait another 0.6 seconds for your action to register.

It seems for basilisks you have to move within the first tick of the attack, and the animation for the attack starts before the red ball appears. So by the time you click it's often too late to actually move since you'll be hit before your movement registers. You can avoid this by moving around them every attack so you're never in the same tile for more than 0.6 seconds but that seems pretty click intensive. My recommendation is to slow the attack by a tick or two so that players can be rewarded (i.e. not frozen) for paying attention, and actually have time to react.