You're missing the point. I wasn't asking "Is Devil May Cry franchise in modern times?", I asked what time period each of the games fall under as time progresses, based on technology such as firearms, vehicles, etc.
People have approached Kobayashi about the technology and time period DMC takes place in, and he agrees with Kamiya and Itsuno's idea of the series taking place in the modern world, but has a few technological setbacks due to it taking place in this alternate, post-war-of-2000-years-ago setting.
In other words, it's
in modern day, and phones and cars exist, but the phones are like old-fashioned dial-up phones, and all the cars and televisions have a 80's-90's look to them. Diners, bars, and strip-clubs have a very 80's and 90's look, but the people in them dress in modern clothes...some of them even having modern cell-phones. Keep in mind that Dante has a bunch of old-fashioned things, like a 50's-style jukebox, but that's probably because he has an appreciation for old-fashioned novelties---hence the old-fashioned bar and pool table.
A good indicator of the series taking place in modern day is Nero's headphones. He has such modern headphones---and is listening to heavy metal, I might add---but the shops and cars in Fortuna have a very old-fashioned look about them.