Turning one’s rida’ inside out should be done during the khutbah of istisqa’ whenthe imam turns his rida’ inside out. .,Prayers on various occasions ,-

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In one of the mosques I saw one of the seekers of knowledge wearing
his 'abayah (cloak) inside before the prayer for rain (istisqa'), and
after the prayer I asked him he reason for that, because what I know
is that the 'abayah should be turned inside out after the prayer and
khutbah are over. He said: There's nothing with that, rather we turned
it inside out before the prayer so thatwhen we changed it again it
would be right side out. What is your opinion concerning this?May
Allaah reward you with good.
Praise be to Allaah.
The apparent meaning of the ahaadeeth narrated from the Prophet (peace
and blessings of Allaah be upon him) concerning the prayer for rain
(salaat al-istisqa') is that the rida' (cloak, upper garment) should
be worn as normal, and it should be turned inside out during the
khutbah when the imam turns hisrida' inside out.
With regard to turning the rida' or 'abayah inside out before that,
the more correct view is that this is not prescribed and is contrary
to the Sunnah. May Allaah help us all.
Kitaab Majmoo' Fataawa wa Maqaalaat Mutanawwi'ah li Samaahat al-Shaykh
'Abd al-'Azeez ibn 'Abd-Allaah ibn Baaz (may Allaah have mercy on him)
– vol 13, p.83.