Is it permissible to perform tayammum for prayer after masturbating in secret, fearing exposure to family upon ghusl, with the intention of performing ghusl later?

It is not permissible to perform tayammum when water is available, except for the sick or those unable to move. What is mentioned in the question does not permit tayammum. Allah permitted tayammum when water is absolutely unavailable, whether at home or during travel, or when there is hardship in using it, such as illness and the like.

The conditions for the validity of tayammum are the absence of water, or the inability to use it due to illness or similar reasons, or fear of harm from using it.

Allah the Almighty said: "O you who have believed, do not approach prayer while you are intoxicated until you know what you are saying, nor while you are in a state of ritual impurity [janabah] except those passing through [a prayer area] until you have washed. And if you are ill or on a journey or one of you comes from the place of relieving himself or you have contacted women and find no water, then seek pure earth and wipe over your faces and your hands [with it]."