Shaykh Sālih al-Fawzān (حفظه الله) was asked about the specified times that an individual is allowed to make the morning, afternoon and night adhkār. He (حفظه الله) responded with the following:

The time for the morning adhkār [begins] from dawn, and the time for the afternoon/night adhkār [begins] from the diminishing of the sun, Ẓhuhr time. All of this is the time in which adhkār is done. All of them [i.e. the adhkar] performed at these times: after the diminishing [of the sun, Ẓhuhr time], after Ẓhuhr [i.e. after the Ẓhuhr ṣalāh], after ʿAṣr [i.e. after the ʿAṣr ṣalāh], after Maghrib [i.e. after the Maghrib ṣalāh] is [considered to be] the night [adhkar].

Therefore, if he makes the adhkār anytime in the night, then he has accomplished making it in its time. Likewise, the morning [adhkar]. If dawn appears [and] he makes the adhkār immediately after dawn—after the Fajr ṣalāh, after sunrise up until the sun is in the middle of the sky [this occurs just before the Ẓhuhr ṣalāh]—then all of this is the time for the morning adhkār.

Source: وقت أذكار الصباح والمساء
Translated by: Abū Wāʾil Musa Shaleem