Yes, as usual always with bacterial colonies, you want to keep them wet through processes and re-stabilized in a running filter in as short a time as is reasonably possible allthough its not an emergency type thing at all. In placing your sponge cuts into the stingray, you just do the best you can. If you observe the stingray having two types of sponge, coarse and fine, then usually you want the mature media to be positioned more like the finer sponge, so that the coarse sponge can have cleared larger debris first. But its ok if you can't get down to those kinds of niceties. The important thing is just getting the mature media in the filter as a hopeful speedup to your cycle.
~~waterdrop~~
edit: remembered you are fishless cycling, so remember, you just continue to follow the Add&Wait guidelines - the mature media doesn't change your actions - you keep adding ammonia back to correct level after it has dropped to zero, keep recording ammonia, nitrite and pH stats in your log etc.
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