It depends on the action against your record. Some reinstatements require proof of financial responsibility on file; others require only that you be insured. Your DMV notice states which, and that is the only reliable source.
More detail
The distinction is real and worth checking rather than assuming the worse case. The DMV's own list varies by action: accident suspensions, for example, need the SR-22 only on the date of reinstatement, while point and court-ordered revocations need it for three years from eligibility. A driver who buys a filing they did not need has paid a small fee and, more importantly, put themselves in a reporting relationship with the state that they did not have to be in. The reverse error is more common and more costly: assuming ordinary insurance is enough when the notice required a filing, and discovering months later that the DMV never received a certificate and the license was never reinstated, since the DMV does not accept a policy, a binder, or an ID card as proof. If the notice is unclear or you cannot find it, the DMV is the office that can read your record back to you. A producer can tell you what a filing involves, but only the state can tell you whether your record requires one.