The cable and the inside of that Twatsoo tiller arm looks like its been down a pit. You want to strip it out and thoroughly clean the assembly then grease the entire length of the throttle cable with a Duckhams yellow grease. My guess it's the friction and gunk that's forcing it to pop out. Is the plastic wheel that the cable grommet sits in worn or damaged? Had the same thing on a Makita strimmer. You could use a little epoxy, but it makes replacing it a little difficult, not that the tiller throttle cable is ever likely to need renewal.