Gibson assembly uses T5 exonuclease to chew back the 5' end of dsDNA to generate overhangs. However, T5 exonuclease, in contrast to lambda exonuclease, is reported to have ssDNA endonuclease activity (https://www.neb.com/products/m0363-t5-exonuclease#tabselect0). Why doesn't his cause problems during gibson assembly? Is it just because these don't yield viable assemblies? Or is it because this activity is inhibited somehow, such as the T5 concentration is too low?
The buffer conditions used in the reaction also mitigate against the endonuclease reaction, so it should not be a problem if you stick to the protocols exactly. I've worked on this enzyme since 1988 and was the original "cloner' of the overproducer see http://www.sayers.staff.shef.ac.uk/fen/ for more information on these enzymes Jon Sayers, University of Sheffield.
I've never actually done a Gibson assembly, but looking over the protocols at the New England Biolabs website, I think the answer must be that the ssDNA exposed by the T5 exonuclease is quickly protected from the ssDNA-endonuclease activity because it (the exposed DNA) anneals with the complementary sequence on the other component of the assembly reaction. Following that, any gaps are repaired and sealed by DNA polymerase and DNA ligase. All of these enzymes are of, course, present at the same time in the one-step assembly reaction.
In summary, under the conditions of the assembly reaction, the low-level ssDNA endonuclease activity of the T5 exonuclease is simply outcompeted by the other reactions taking place.