Hello Friends 
In my API response i am getting String Field Date_modified=08/23/2019
i would grab this field and assigning to Datetime Field called Acct_Modifieddate.
Datetime Acct_Modifieddate =date.parse(Date_modified);
In the log i see Acct_Modifieddate as 2019-08-23 00:00:00.
And finally i would be pushing this field to another Datetime custom field via process builder.
In the Salesforce UI i see this field populated as 8/22/2019 5:00 PM

Please advice whether this problem related to GMT timezone issue or something else.

Thanks