The plugin uses annotated tag's commit timestamp instead of tag created timestamp and use it to compare with the value in the setting "Ignore tags older than".

Environment:
Jenkins v2.235.5
Basic Branch Build Strategies Plugin v1.3.2
Bitbucket v6.10.0

To Duplicate this issue,
1. Set "Ignore tags older than" to 3 and "Ignore tags newer than" to empty string in the project configuration
2. Create an annotated tag on a commit older than 3 days.
3. Observe that the tags tab creates a job for the created annotated tag but it doesn't build. It is expected to build, as the tag creation time is less than 3 days and as per the inline help message - "The number of days since the tag was created after which it is no longer eligible for automatic building".
4. The behavior is same on the annotated tags

I hope the expected behavior is to consider the tag creation time (not the associated commit time of the tag) for build strategy comparison.

it makes sense, I think we need to create annotated tags would actually trigger the job build automatically.

if people created the lightweight tags, you should note that the tag created date would be last commit date

Note:  date of tag creation for annotated tags and the date of the last commit for lightweight tags:
https://github.com/jenkinsci/git-plugin/blob/master/src/main/java/jenkins/plugins/git/GitTagSCMHead.java#L37-L38

Here is where the plugin tests dates and it uses the "timestamp" of the tag:
https://github.com/jenkinsci/basic-branch-build-strategies-plugin/blob/master/src/main/java/jenkins/branch/buildstrategies/basic/TagBuildStrategyImpl.java#L152

It is up to the the implementers of TagSCMHead to provide that:
https://github.com/jenkinsci/scm-api-plugin/blob/master/src/main/java/jenkins/scm/api/mixin/TagSCMHead.java

The git plugin does what Mark Waite described - use the date of tag creation for annotated tags and the date of the last commit for lightweight tags:
https://github.com/jenkinsci/git-plugin/blob/master/src/main/java/jenkins/plugins/git/GitTagSCMHead.java#L37-L38

This comment on SO repeats what Mark Waite said:

There is no date information attached to a lightweight tag. ... The dates in the output of git log --tags --simplify-by-decoration --pretty="format:%ai %d" are the dates of the objects to which the tags point, not the dates when the tags themselves were created.

I think either of the command above would have this same problem, but you'd need to test them to be sure. Further, it is likely that this behavior will differ depending on the underlying branch source - git, github, bitbucket, etc.

i think 

1. command gives the tag created date 
    git for-each-ref --format="%(refname:short) | %(creatordate)" refs/tags/*
2. Command returns the commit id date for tags

git log --date-order --graph --tags --simplify-by-decoration --pretty=format:'%ai %h %d'
Not sure which one plugin uses to analyse the date?

ok do we have any way to get the actual tags created date stamp? I think to use this plugin that date will be an appropriate one?