When someone from the future travels to the past and changes something, existence in the path they are in does not cease to exist, but the dimension of time from which they travelled will be destroyed. The potential for the future to remain in existence is dependent on whether the traveller changes anything in the past. The mere presence of the traveller, however, would change even the most minor details of existence, that for all practical purposes, we should assume that the time dimension from which the traveller is from will be destroyed the instant they "step outside" of that time dimension. This is not so much time-travelling - that is, going "back and forth" on the same time line - the travellers would be time-dimension jumpers. They "jump" from one time dimension into another parallel time dimension that they alter. So, original ends, new one changes.
Their own status as existing is not affected, as their existence is now only dependent on the new time dimension's ability to sustain them. They are now part of the new time dimension reality, based entirely on the fact of their present existence. Their original time dimension remains unaltered - their a priori existence is therefore not affected. It just happens to be that the time dimension ends with their exit - it doesn't cease to exist, it just comes to an end. The traveller's existence is now only contingent on the fact of their being, not being born in the time dimension in which they find themselves. Existence contingent on being born is only a factor when you exist in your own, original, time-dimension. Essentially, once you exist, you will exist, by the fact that you do exist. Your birth-time-dimension has already facilitated your existence.
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