Yes, we can achieve this using SSIS.
You need to create a data driven subscription in your SSRS report which will extract the excel sheet and send it via Email.
In SSIS, you can add SQL Task to trigger this subscription after completion of load in your tables.
You can use this query on report server to execute your SSRS report subscription using SSIS:
DECLARE @vchSubscriptionJobName AS VARCHAR(500)
SELECT @vchSubscriptionJobName = Schedule.ScheduleID
FROM dbo.ReportSchedule
INNER JOIN dbo.Schedule
ON ReportSchedule.ScheduleID = Schedule.ScheduleID
INNER JOIN dbo.Subscriptions
ON ReportSchedule.SubscriptionID = Subscriptions.SubscriptionID
INNER JOIN dbo.[Catalog]
ON ReportSchedule.ReportID = [Catalog].ItemID
AND Subscriptions.Report_OID = [Catalog].ItemID
WHERE [catalog].name = <<Report Name>>
EXEC msdb.dbo.sp_start_job @vchSubscriptionJobName
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AP