I do similar, but frame it in terms of dependencies.
The database can live without the web server, but the web server doesn't work without the database.
Therefore webserver ---> database.
Key thing in that these deployment / context / container diagrams don't have a temporal axis. If you want to represent a flow, then you want a diagram where time has directionality, like a sequence diagram.
Comments
I do similar, but frame it in terms of dependencies.
The database can live without the web server, but the web server doesn't work without the database.
Therefore webserver ---> database.
Key thing in that these deployment / context / container diagrams don't have a temporal axis. If you want to represent a flow, then you want a diagram where time has directionality, like a sequence diagram.