Travel Through Space and Time
SP creatures are able to travel outside of their universe, and into alternate timelines (post Kosmotvar Crisis upon obtaining the ability via the Time Hole). However, they have certain backup measures to prevent them from being stuck in another reality, space, or time when they want to leave.
Every SP creature carries a bit of their own reality within their heart. This reality consists of two halves, the reality of the universe the creatures come from (the same universe as Earth), and a bit of their own unique reality that no one has access to but themselves. In the worst case scenarios, the SP Heart can warp the creature back to one of the two realities willingly or unwillingly (if the creature is somehow incapacitated, or heart is somehow at risk despite not being able to be destroyed). If something is wrong with the universe SP is located in, the heart will go to the last resort measure, and use the unique reality within the creatures heart and cast it around the creature. This reality is initially empty, and can be used to protect the creature, not allowing anything/anyone else in unless the creature decides it's reasonable.
As for time travel, the heart performs the same functions in risky scenarios, putting the creature back into the current timeline as well if it is possible. With time travel, a bit more specifications apply, as the SP creatures only age based on the universe Earth is located in. Even if a creature goes to a universe for five minutes where the flow of time is one hundred times faster, once returned, the creature would have only aged five minutes. Additionally, SP creatures are able to sense if there are any events happening that are not native to their timeline, and are able to organize the things they have seen (from both future and past) into separate memories not to confuse them with current memories.
Since there is only one instance of every SP creature per universe, duplicates cannot be created from any kind of travel. If an alternate timeline is created, eventually all creatures can be synced up and merged into one true creature with knowledge of both timelines.