Does that mean that I have 30 days to recover my domain?
Absolutely not.
What you quote (redemption grace period) is what happens after a domain is deleted not after it expires, because in fact at expiration it is automatically renewed.
Expiration process in gTLDs
But let us go into more details on how things happen, typically in gTLDs:
- your domain arrives at expiration
- at this point typically your contract with the registrar ends; what happens now depends on what is written in this contract; ICANN gives some rules, the registrar is also constrained by registries, but even so you will find a lot of variations on what happens after
- for the registrar point of view, the domain is now in the "Auto-Renew Grace Period": the registry has renewed the domain name (this can be seen if you do a whois or RDAP query), and gives the registrar a delay (which is now de facto 45 days) during which the registrar can delete the domain to get a full refund by the registry; if the registrar does not do anything and the delay ends, then the domain is really renewed and stays like that
- for the registrant point of view, what happens depends on the registrar and his contract with him; he paid until the expiration, what happens next is at the will of the registrar
- here are various cases that happen: besides various emails to warn of the expiration, the registrar can put the domain on hold which will cut all services (the domain will appear as if not published in the DNS), or change the domain nameservers to point the website to a page stating the domain is expired, or put the domain on auction and resell it to the highest bidder; the fee to renew after expiration can also vary depending on the delay after expiration
- some registrars may give you 30 days or less, even if they have themselves 45 days given by registry: they are in no way required to pass that to the registrant to let him make his choice, specially since the registry can/may/will bill the registrar for the auto-renewal at the date of expiration
For gTLDs, registrars are bound by ICANN policies:
At the conclusion of the registration period, failure by or on behalf
of the Registered Name Holder to consent that the registration be
renewed within the time specified in a second notice or reminder
shall, in the absence of extenuating circumstances, result in
cancellation of the registration by the end of the auto-renew grace
period (although Registrar may choose to cancel the name earlier).
and
In the absence of extenuating circumstances [...], a domain name must
be deleted within 45 days of either the registrar or the registrant
terminating a registration agreement.
Subject to applicable consensus policies and provisions of the
Registrar Accreditation Agreement ("RAA"), registrars may delete
registrations at any time after they expire.
and
Registrars must make their renewal fees, post-expiration renewal fees
(if different), and redemption/restore fees reasonably available to
registered name holders and prospective registered name holders at the
time of registration of a gTLD name.
Deletion in gTLDs
What you quote is about deletion. A domain can be deleted at any time by registrar: either because the client asks for it, or some disputes, or to make sure it is not renewed again (see above) because the client just did not pay for the extension of registration.
If the deletion is done during the 5 days after the domain creation (this is called the "add-grace period"), then it is immediate, there is no redemption.
If it is done at other time, a redemption kicks in: to safeguard around erroneous deletions, a registrar can ask the registry to undo the delete which is called restoring the domain. To deter people from using this regularly the price of this operation is often around 10 times the price of a normal one year registration or renewal. It is really the last minute option in case of errors and defects.
You can see ICANN domain name lifecycle here:
https://www.icann.org/resources/pages/gtld-lifecycle-2012-02-25-en
and the image is included below:

Have a look also at http://icann.org/epp that details the status codes that you can see in a reply to a whois or RDAP query on your domain, and they will show if you are in any grace period, so if renewal is still possible, if deletion has been started, and if you are still in redemption grace period or not.
In summary of all the above there is strictly no reason to wait for the last moment to renew: if you renew a domain you add years to the current expiration date so the end result is the same whatever moment you decide to do. Waiting the last minute is only increasing the risk of problems, so this should be avoided. Of course important domains should not even be registered for one year and renewed each year, but registered for example for 5 or 10 years (ICANN maximum)