Why Flutter IconButton Animation Shows Under the Row

The ripple is part of the Material effect. Wrap your IconButton with Material:

Material(
  color: _bgColor,
  child: IconButton(
    padding: EdgeInsets.only(right: 16),
    icon: Icon(Icons.play_arrow, color: Colors.white, size: 48),
    tooltip: 'Start ${issue.issueName}',
    onPressed: () {},
  ),
),

---

UPDATE

To be more specific to your goal, you can replace your Container with Material.

return Material(
  color: _bgColor,
  borderRadius: BorderRadius.all(Radius.circular(10.0)),
  child: Container(
     margin: EdgeInsets.only(top: 12, left: 18, right: 18),
     padding: EdgeInsets.only(top: 8, bottom: 8),
     backgroundBlendMode: BlendMode.multiply,
     child: Row(
     ...
  ),
);

It looks like a bug in the Flutter Framework. This occurs only with IconButton, no problem with FlatButton.

Possible workaround is to set BlendMode to multiply BlendMode.multiply.
try this:

Container(
          decoration: BoxDecoration(
              color: Colors.greenAccent[400],
              backgroundBlendMode: BlendMode.multiply),
          child: ListTile(
            leading: IconButton(icon: Icon(Icons.play_arrow), onPressed: () {}),
            title: Text("issue title"),
            subtitle: Text("description"),
          ),
        ),

Update
issue on github