The adhkar of evening start after the sun passes the zenith (at the beginning of the time for Zuhr/afternoon prayer) until the sun sets, and at the beginning of the night. The adhkar of the morning start from the break of dawn until the sun passes the zenith. Allah says (interpretation of the meaning):
“... and glorify the praises of your Lord before the rising of the sun, and before its setting.”
“And remember your Lord within yourself, humbly and with fear and without loudness in words in the mornings and in the afternoons.”
“afternoon” means between ‘Asr and Maghrib.
And Allah says (interpretation of the meaning):
“So glorify Allah [above all that (evil) they associate with Him (O believers)], when you come up to the evening [i.e. offer the (Maghrib) sunset and (‘Isha) night prayers], and when you enter the morning [i.e. offer the (Fajr) morning prayer].
And His are all the praises and thanks in the heavens and the earth; and (glorify Him) in the afternoon (i.e. offer ‘Asr prayer) and when you come up to the time, when the day begins to decline (i.e. offer Zuhr prayer).”
[al-Room 30:17, 18]
And Allah is the Source of strength, may Allah send peace and blessings upon our Prophet Muhammad and his family and Companions. End quote.
Standing Committee for Academic Research and Issuing Fatwas
Fatawa al-Lajnah al-Daimah li’l-Buhooth al-‘Ilmiyyah wa’l-Ifta (24/178)
See also question no. 22765.
And Allah knows best.