Since the source of truth resides on your Database and you push data from this DB to Redis, you always have to update from DB to Redis, at least you create another process to sync data.
My suggestion is just to run a first full update from DB to Redis and then use a synch process which every time you notice update/creation/deletion operation in your database you pull it to Redis.
I don't know which Redis structure are you using to store database records in Redis but I guess it could be a Hash, probably indexed by your table index so the sync operation will be immediate: if a record is created in your database you set a HSET, if deletion HDEL and so on.
You even could omit the first full sync from DB to Redis, and just clean Redis and start the sync process.
If you cannot do the above for some reason you can create a syncher daemon which constantly read data from the database and compare them with the data store in Redis if they are different in somehow you update or if they don't exist in some of both sides you can delete or create the entry in Redis.