Let's take a look at the language of the commandment:
Exodus 20:8-11 Remember the sabbath day, to keep it holy. Six days shalt thou labour, and do all thy work: But the seventh day is the sabbath of the Lord thy God: in it thou shalt not do any work, thou, nor thy son, nor thy daughter, thy manservant, nor thy maidservant, nor thy cattle, nor thy stranger that is within thy gates: For in six days the Lord made heaven and earth, the sea, and all that in them is, and rested the seventh day: wherefore the Lord blessed the sabbath day, and hallowed it.
Within thy gates. It comes down to personal responsibility. As the commandment specifies, it is your responsibility to observe the Sabbath in your own household and ensure anyone within your gates observes it as well.
It is another person's responsibility to observe Sabbath in their own household, within their own gates and make the necessary preparations to ensure it is able to be observed. You have no control over another person in another time zone, nor should it be your responsibility. E-mail would be the same. A person observing the Sabbath probably isn't going to be checking on their business e-mails, but even if they do glance at their phone or computer, they can put the device down or step away from it without reading it.
On the flip side, say you order something from Amazon.com during the week, but it shows up on Saturday. Usually, ship date and arrival date is specified, but there are times when I have had packages arriving on Saturday and there's no way to keep it from happening. It's not something I set out to do, to cause someone else to work on Sabbath and deliver a package to me. Even if you order on a Sunday or Monday, sometimes the package still doesn't arrive until Saturday, despite the actual specified ship date. The Amazon deliverer would be "within thy gates", delivering my package on the Sabbath. Does it mean a stranger who is a guest or a stranger momentarily delivering a package? I think it means both. We should do everything we can to make sure a package arrives outside the Sabbath day.
Since we are staying home during Sabbath, aside from church, being out in nature, fellowship, or the Lord's work, we are generally not causing others to work for us on the Sabbath. i.e. We don't go out to eat, we don't go to a store to buy and sell, etc. But when we are out, we do the same as if we were at home, within our gates.
There are things that are beyond your control and that are not your responsibility. You should endeavor to ensure your own household is in observance and that you are not causing others to work for you during
your observance. Each person is responsible for their own observance.
Others may have a different view on this. At the end of the day, we each do according to our conscience, based on scripture. I think it comes down to what you take from scripture. Pray on it and ask for guidance.
God bless and Happy Sabbath!