Yes, corporeal atomism in fact implies temporal atomism. Not rarely is it maintained that if one of the following five concepts is seen as atomic, the other four have to be atomic in nature as well:
The claim that these concepts stand and fall together could be traced back to Aristotle (d. 322 BC), who wrote in the discussion of time in Physics IV.10--14 that time follows motion, which follows the magnitude/distance/extension over which the motion occurs. The Greek for "follows" is ἀκολουθεῖ (akoluthei), translated into Arabic by تبع (tabaʿa) / تابع (tābiʿ) or طابق (ṭābaqa) / مطابق (muṭābiq). However, of course, Aristotle used this argument to corroborate the exact opposite of atomism, namely, that neither motion nor time nor magnitude is atomic but rather continuous (συνεχής, sunechês; متّصل , muttaṣil) in nature.
Elaborations on the atomicity of these five things could be found, e.g., in the writings of Faḫr al-Dīn al-Rāzī (d. 606/1210; cf. his al-Maṭālib al-ʿālīya min al-ʿilm al-ilāhī, Vol. 6, p. 29), but actually discussions of this sort are rather common and could be found in the respective sections on body and time in many other kalām-writings, though maybe not always as explicit as in the case of Faḫr al-Dīn.
The argument basically is that if, e.g., the world is atomic in structure, then any distance is atomic, too. Accordingly, your traveling from Baġdād to London happens from one atom to another atom to another atom to another atom. So, your entire motion would be atomic. Thus, the time, which measures your motion, would likewise be atomic like seconds, etc.
Of course there are also thinkers, e.g., Avicenna (d. 428/1037; not an Ašʿarite), who argue for the alternative (and more Aristotelian) conception that the world is intrinsically continuous, thereby rejecting atomism altogether. These thinkers use the same line of argument to claim motion, time, body, distance, and space to be continuous together.
One note of caution: Greek atomism should not be confused with Islamic atomism. Even though there is some influence of Greek, especially Democritean, atomism on its Islamic cousin, the foundations and much more so the reasons for atomism in Muslim doctrines are very dissimilar and indeed quite unique.
More information could be gathered from Wolfson, The Philosophy of the Kalām; and Dhanani, The Physical Theory of Kalām.