they arrived at the same time : SIMULTANEOUSLY, at the same instant/moment, together, all together, as a group, at once, at one and the same time; in unison, in concert, in chorus, as one.
I can't really explain it, but at the same time I'm not convinced : NONETHELESS, even so, however, but, still, yet, though; in spite of that, despite that, be that as it may, for all that, that said; notwithstanding, regardless, anyway, anyhow; informal still and all.
2192; headword