He did say something about self directed, so it may be a self directed IRA.
Is it possible that he is just TRANSFERRING (rather than contributing) money from an already existing IRA to this? If the 5498s show the balance is remaining the same, that is what makes sense to me.
You need to ask the client (and if the does not know, they need to contact this company) who is the "custodian" of the IRA. This company may just merely be mechanism of investment and the client has some other "custodian" for the self directed IRA.
For example, a person may have the brokerage Charles Schwab as the "custodian" of a regular IRA, but that money may be invested in to buying Microsoft stock. Likewise, your client could have an already existing $60,000 of IRA (from previous IRA contributions) invested in a Charles Schwab type of company (that deals with self directed IRAs) that is just investing in this company.