It has to take the Dash action if doing so results in the turned creature being further away from that which turned it
The fact that it must "spend its turns trying to move as far away from you as it can" implies that, if taking the Dash action would enable it to move further away from you, since it has to "move as far away from you as it can", then it must use the Dash action in order to do so. Avoiding taking the Dash action would imply that it isn't doing all it can to move further away from you, which contradicts that quoted statement.
The only reason it wouldn't have to take the Dash action blindly, or rather, why the features don't "force" the turned creature to take the Dash action, is because if doing so wouldn't actually result in the creature being any further away from you, say, because it is cornered, then doing so doesn't really comply with moving as far away from you as it can, so there's no reason for it to do so.
The Turn Undead and Turn the Faithless features both go on to say (PHB, p. 59 and p. 87):
If there's nowhere to move, the creature can use the Dodge action.
If the creature had to use the Dash action blindly, regardless of context, then there'd be no reason to include this option. So, if a creature uses its normal movement to run into a corner, then it could then take the Dodge action instead if the Dash action wouldn't actually help it to move further away.