Till and until both mean during a period ending at a particular time. The time could be specified directly, or by referring to an event which will define the end of the period. .
"She is staying in Llandudno till Saturday." means she will be there for the entire period up to Saturday.
"She is staying in Llandudno till after Saturday" means she will be in Llandudno for the entire period up to and including Saturday, and will not leave until some time on Sunday or Monday, or even much later. If we are also in Llandudno we might ask to meet her on Saturday evening.
"I will love her till I die" is another way of saying I will love her for the rest of my life.
"I will wait on the platform until the train arrives" means I will remain here until that event happens.
She was in the bathroom from 7.15 till 8.30" means she was in the bathroom all the time between 7.15 and 8.30.
Until could be used instead of till in all the above examples. There is no difference between till and until. Many people nowadays consider till to be informal, but the Registration Act of 1908 was not an informal document.
In the phrase in the Registration Act "is not presented until after the expiration of the time", the time means the time during which the document should be registered. Most types of document should be registered within four months from when they are signed. So if a particular document was signed on the last day of January it should be registered by the end of May. It should be registered at any time in February, March, April or May. and the expiration of the time is the end of May.
The document is not presented till it is presented. We are not dead until we die. The document is not presented until X, means that X marks the end of the period during which it is not presented. A much simpler way of saying "is not presented until Thursday" would be "is presented on Thursday".
If the Act had said "is not presented until the expiration of the time" this would mean, in our example, it was not presented until the end of May. It would be saying what should happen if the document was presented right at the last minute. If it is not presented until the last minute the registrar shall wag his finger and exclaim, "you are almost late!", for example.
Using the words "is not presented until after the expiration of the time" is another way of saying that the time at which it is presented is after the end of the period in which it should be presented. More simply, it is talking about what the registrar should do if the document is presented late.
There is also a difference between "is not presented by" and "is not presented until after". If the Act wanted to specify what should happen if our example document had not been presented by the end of May we would know, on June 1st, that something should be done about it. It would make no difference whether the document was presented late, or there was no intention of ever presenting it, By using the phrase "is not presented until after" it makes clear that it is referring to what to do when a document is presented late. (It may be accepted, subject to conditions, and for an extra fee.)
"Till before" is sometimes said. For example we could say "don't put the kettle on till before teatime" and this would be taken to mean "don't put the kettle on until just before teatime". A pedantic, or thirsty, person could point out that it is before teatime now, but in this context before means just before.