Oh My Zsh multiple commands with one alias

As you've discovered, you can chain commands in a single alias using ;:

alias update_my_gems="echo foo; echo bar"

Alternatively, you can write a function very easily in your ~/.zshrc file:

update_my_gems() {
    echo foo
    echo bar
}

For readability, I'd personally go for a function for anything that's semi-complex.

If there are many commands, I find it useful to alias the execution of a .sh file located on my home directory

alias start_containers="./start-containers.sh"

To throw the alias inside the config file, you can do

echo alias start_containers="./start-containers.sh" >> ~/.zshrc