Not necessarily, the offer could be amended and increased that's perfectly normal and still not hostile. Hostile is when you pursue against the wishes of the current owners of the company and their management, so in other words if they have indicated that they are either not for sale or that they are not going to sell their shares to you.

You could then try for a hostile takeover by buying up as much as you can on the open market and possibly to try to get one or two smaller shareholders to sell their shares to get you more than 51% (and in some cases more than 66% aka a supermajority) to be able to call the shots.

Even then, the Twitter board has staggered terms, so it is impossible to do a wholesale replacement of the board and thereby gain control of Twitter. The board voted unanimously to invoke the poison pill provisions in the bylaws so it isn't a matter of swaying a small number of board members.

Tender offers can be hostile - a "hostile tender offer" is an offer directly to shareholders to buy shares at a certain price, without getting the blessing of the board.