The tag opens a search instead of my site
The address was written without its scheme, so nothing in the record identifies it as a web address. A phone handed bare text has no instruction to open anything at all, and what happens next depends on the device rather than on your intention.
The scheme is what makes it a link
An address written as a web address record carries a scheme, and the standard stores the common ones as a single byte rather than as text. That byte is what tells a reader this is a web address.
Write the same characters without a scheme and the record has no such indication. The phone receives something that looks like an address to a human and carries no instruction for a machine.
Typing a bare domain into a writing tool is how this happens. It looks complete and it is missing the part that matters.
Or it was written as text
A text record is content to display, not an action. An address written as text is read, shown, and not opened.
This is easy to do by accident in a tool that offers several record types, particularly if the text option is the default or the first in a list.
Read the tag and check the record type rather than the content. The content will look right in both cases, and only the type distinguishes them.
Some phones offer to open an address they recognise inside a text record, and that is a courtesy rather than a guarantee. It is exactly the behaviour that varies between devices.
Why behaviour varies by phone
With no instruction attached, each system decides for itself. One opens a browser, one runs a search, one shows the text and stops.
So a tag can work on the phone you tested with and behave differently in a visitor's hand, which is the worst failure mode: it passes testing and disappoints in the field.
Nothing about this is fixable at the phone end. The tag has to say what it is.
Writing it properly
Choose the web address record type explicitly rather than accepting a default.
Include the scheme in what you type. A tool that adds it for you is helpful and not universal, so typing it is the reliable habit.
Use the secure scheme. Browsers treat plain addresses less favourably, and there is no capacity reason to prefer one since both are stored as a single byte.
Then read the tag back and check the reported record type, not just the text. And tap it on a phone that is not the one you wrote it with, which is where this fault shows itself.
Frequently asked questions
Why does it work on my phone and not others?
Because a record with no scheme carries no instruction, so each system decides for itself. Consistent behaviour requires a proper web address record.
Does https cost more space than http?
No. Both are stored as a single byte by the prefix abbreviation, so there is no capacity argument for either.
Can I write just the domain?
You can, and it produces exactly this problem. Include the scheme so the record identifies itself as a web address.
How do I check which record type is on the tag?
Read it with a tool that reports record types. The text looks identical either way, and only the type tells you what will happen.