Obviously back up (download) all your emails first via POP3 to your PC, if you only use IMAP to connect to your inbox you'll lost all your old emails when you migrate away.
Sounds like you need to update your DNS records to have correct MX entries. Have you migrated the DNS to TsoHost, or did you buy the domain separately?
I now buy domains separately (usually the excellent Namesilo for anything non .uk, Heart Internet for anything else though I'm contemplating migrating all my .uk to a competitor called 20i, as a few other people have done). Then, on the control panels on the registrar services, I point the domain's DNS settings to a host's DNS servers if I'm using them for email / web hosting etc. Otherwise I set them to my own DNS servers.
Sidenote: I've used afraid.org for years as a completely separate DNS provider. The update speed is impressive, the network design is very resilient and the customer support is good. It's admittedly a niche service but it's exactly what I need. I pay a few bucks a year for premium. Amongst other things, this lets me 'stealth' domains so other free users can't see them and request to set up subdomains on them - one of the core features of the free service. Afraid's early raison d'etre was to provide free DDNS services based on people sharing their domains.)
Email works by relying on MX records to tell sending mailservers which physical machine (on a particular IP address) is handling email for an address. So in addition to things like the standard "A" records (IP addresses) and "CNAME" records (just aliases for other domains), email relies on "MX" (Mail eXchanger) records.
Say I have an email server running with
[email protected] at IP address 1.2.3.4. I need to make sure that whichever DNS server looks after queries for 'myserver.com' must have these records at least:
An "A" record for the 'root' (which equates to myserver.com) for 1.2.3.4
An "MX" record for 1.2.3.4 (usually in the format 0:myserver.com -- the first digit is the 'costing', or priority, lowest is tried first)
Other records like SPF, DKIM and DMARC are also recommended these days, to do things like verify sending server is authorised to send emails (curbs some spam) and that emails are verifiably from the sender and haven't been modified en route (DMARC). Some of this is done on the actual server, some of it is "TXT" format DNS records.
How emails get to an address:
The mail server sending an email to '
[email protected]' first does a DNS query for "myserver.com" to identify which DNS servers are serving queries for the domain. It then queries that DNS server for its MX records, receives either a CNAME record in response (which it has to resolve again to the actual IP address) or an A record, which is the IP address, in response. It then connects to the receiving mail server sat on that IP address and attempts to deliver the email.
If you have multiple MX records with conflicting mailserver details, some of your emails will likely be going astray (into the wrong mailserver's receive queue) if both MX records have an equal weighting.
More importantly, a random number of emails intended for an address will likely be bouncing because they're arriving at the mailserver which isn't handling that particular account.
Use
https://toolbox.googleapps.com/apps/dig/#MX/ and put in your email domain name. If in the response you see the 123-reg servers is like this for example:
;ANSWER
mydomain.com. 3599 IN MX 0 mx1.123-reg.co.uk.
mydomain.com. 3599 IN MX 10 mx2.123-reg.co.uk.
Then your DNS records are still instructing sending servers to route email traffic to the wrong mail server.
You can't have two third party providers with unconnected mail servers separately hosting different addresses on the same domain. Unfortunately, that's the preserve of a clustered mailserver setup which is well beyond what you'll get from either Tso or 123.
Tso have some useful FAQs:
https://help.tsohost.com/knowledge-base/article/4344
https://help.tsohost.com/knowledge-base/article/5152
https://help.tsohost.com/knowledge-base/article/4370
Some recommend additional A and MX records for "mail.myserver.com" but frankly I don't bother with these for my domains which all run with a single mail server, IMO it's a waste of DNS lookups for the sending server when you have a simple all-in-one website, email and DNS setup (which is what most webhosts are). I have no problems with email deliverability doing this on servers I run myself, though there are arguments for adding more DNS records for "mail", "smtp", "imap" etc.
